THE  ELECTRIC  ARC. 


By    HERTHA    AYRTON, 

MEMBER   OF   THE   INSTITUTION   OF   ELECTRICAL    ENGINEERS. 


Of    THF 

UNIVERSITY 


NEW  YORK  : 

THE     D.     VAN     NOSTRAND     COMPANY, 
23,  MURRAY  STREET,  AND  27,  WARREN  STREET. 

LONDON: 
THE  ELECTRICIAN"  PRINTING  AND  PUBLISHING  COMPANY 

LIMITED, 
SALISBURY  COURT,  FLEET  STREET,  B.C. 

[All  Rights  Reserved.] 


' 


Printed  and  Published  by 

1  THE  ELECTRICIAN  "  PRINTING  AND  PUBLISHING  CO.,   LIMITED 

1,  2,  and  3,  Salisbury  Court,  Fleet  Street, 
London,  B.C. 


PREFACE. 


*TPHIS  book,  which  owes  its  origin  to  a  series  of 
articles  published  in  The  Electrician  in  1895-6, 
has  attained  to  its  present  proportions  almost  with  the 
growth  of  an  organic  body.  In  experimenting  on  the 
-arc,  my  aim  was  not  so  much  to  add  to  the  large 
number  of  isolated  facts  that  had  already  been  dis- 
covered, as  to  form  some  idea  of  the  bearing  of  these 
upon  one  another,  and  thus  to  arrive  at  a  clear  con- 
ception of  what  takes  place  in  each  part  of  the  arc  and 
•carbons  at  every  moment.  The  attempt  to  correlate 
all  the  known  phenomena,  and  to  bind  them  together 
into  one  consistent  whole,  led  to  the  deduction  of  new 
facts,  which,  when  duly  tested  by  experiment,  became 
parts  of  the  growing  body,  and,  themselves,  opened 
up  fresh  questions,  to  be  answered  in  their  turn  by 
experiment.  Thus  the  subject  grew  and  developed  in 
what  might  almost  be  called  a  natural  way. 

From  the  first  it  seemed  to  me  that  the  fact  that 
the  resistance  of  the  material  in  the  gap  between  the 
carbons  must  not  only  depend  upon  the  current,  but 
that  it  must  depend  upon  it  in  many  apparently  contra- 
dictory ways,  could  not  but  lead  to  curious  complications 


iv.  PREFACE. 

in  the  relation  between  the  P.D.  and  the  current — quite 
apart  from  any  back  E.M.F.  that  the  arc  might  possess, 
In  the  attempt  to  disentangle  the  various  effects  on  this 
resistance  that  a  change  of  current  must  produce,  and 
to  see  how  far  all  that  was  apparently  mysterious  in  the 
arc  might  be  the  natural  result  of  such  complexity  in 
the  resistance  of  a  portion  of  the  circuit,  the  theory 
presented  in  Chapter  XII.  gradually  evolved  itself. 
This  theory,  whatever  may  be  its  shortcomings,  has  at 
least  not  been  hastily  built  up  to  fit  a  few  of  the  more 
salient  characteristics  of  the  arc  ;  it  has  literally  evolved 
itself,  during  the  course  of  a  detailed  study,  from  many 
points  of  view,  of  each  separate  phenomenon.  For 
although  the  central  idea,  that  the  carbon  vapour 
changed  into  mist  at  a  short  distance  from  the  crater, 
occurred  to  me  at  a  very  early  period  of  the  work,  its 
complete  application  to  the  whole  series  of  phenomena, 
and  the  full  recognition  of  all  that  it  entailed,  followed 
but  slowly,  as  each  part  of  the  subject  was  considered 
in  turn. 

The  experiments  of  other  observers  have  been  em- 
ployed in  two  ways:  (i)  In  confirmation  of  theory 
developed  from  my  own  experiments,  and  (2)  as  the 
basis  of  theory,  for  which  further  tests  were  devised. 
The  law  connecting  P.D.,  current,  and  length  of  arc,  for 
instance,  was  first  constructed  from  my  own  results,  and 
then  was  shown  to  be  applicable  to  those  obtained 
much  earlier  by  Messrs.  Edlund,  Peukert,  Cross  and 
Shepard,  and  Ayrton.  The  theory  concerning  the  light, 
on  the  other  hand,  was  entirely  deduced  from  the 
experiments  of  others.  M.  Blondel's  interesting  and 
systematic  researches,  the  admirable  work  of  Mr.  Trotter, 
and  Prof.  Ayrton's  Chicago  Paper  were  all  laid  under 


PREFACE.  v< 

contribution,  and  the  deductions  drawn  from  them  were 
then  tested  by  new  experiments. 

In  seeking  to  compare  my  results  with  those  of  other 
observers,  and  in  searching  for  accounts  of  experiments 
that  might  furnish  material  for  theory,  I  have  often  been 
struck  with  the  excellent  work  that  has  been  done  by 
men  whose  names  are  quite  unfamiliar  to  us  in  England. 
There  are  admirable  Papers  on  the  arc,  for  instance,  by 
Nebel,  Feussner,  Luggin,  Granquist,  and  Herzfeld,  to 
which  reference  is  seldom  seen  in  any  English  publi- 
cation ;  while  other  work,  which  is  in  some  cases  far 
inferior,  is  constantly  quoted.  I  have,  therefore,  given 
in  Chapter  II.  short  abstracts  of  most  of  the  impor- 
tant Papers  on  the  direct-current  arc  that  appeared 
up  to  the  end  of  the  nineteenth  century,  while  those 
referring  principally  or  entirely  to  the  light  are  discussed 
in  Chapter  XL  At  the  end  of  Chapter  II.  is  a  chrono- 
logical list  of  all  the  original  communications  that  I 
could  find  when  that  chapter  was  written  ;  but  the 
names  of  a  few  to  which  my  attention  has  since  been 
directed,  and  of  some  that  appeared  after  the  list  was 
made,  together  with  the  dates  of  my  own  contributions 
to  The  Electrician .  and  to  various  societies,  are  added  at 
the  end  of  the  Appendix.  The  latest  paper  of  all — 
an  extremely  interesting  one  "  On  the  Resistance  and 
Electromotive  Forces  of  the  Electric  Arc,"  read  by 
Mr.  Duddell  before  the  Royal  Society  in  June  last — 
I  should  much  have  liked  to  discuss  in  connection  with 
this  book,  but,  as  it  is  not  yet  published  in  full,  that  is 
unfortunately  impossible. 

As  it  seemed  better  not  to  wait  till  the  whole  book 
was  ready,  before  publishing  the  most  important  of  the 
new  results  obtained,  some  part  of  almost  every  chapter 

A2 


vi.  PREFACE. 

has  been  made  the  subject  of  a  Paper  that  has  been  read 
before  one  or  other  of  the  societies  interested  in  such 
work.  These  Papers  generally  covered  but  a  portion 
of  the  ground,  however,  giving  the  main  experiments 
and  conclusions  only,  without  following  them  up,  or 
showing  how  they  bore  upon  one  another.  In  the 
book  these  are  all  connected  together,  and  many  new 
results  are  set  forth  which  have  been  developed  during 
the  process.  At  the  end  of  each  chapter  is  a  summary 
of  the  most  important  conclusions  reached  in  it,  which, 
it  is  hoped,  may  be  found  useful  in  making  each  step 
perfectly  clear  before  the  next  is  taken. 

Besides  the  light  experiments  already  mentioned,  all 
those  on  the  time-change  of  P.D.  immediately  after 
starting  the  arc,  and  after  sudden  changes  of  current 
originally  formed  part  of  Prof.  Ayrton's  ill-fated  Chicago 
Paper,  which,  after  being  read  at  the  Electrical  Congress 
in  1893,  was  accidentally  burnt  in  the  Secretary's  office, 
whilst  awaiting  publication.  These  highly  important 
experiments  were  not  only  the  first  of  their  kind,  but, 
as  far  as  I  know,  they  still  remain  unique.  Most  of  the 
figures  in  the  first  chapter,  all  the  experiments  and 
curves  that  relate  to  cored  carbons  in  the  fourth  and 
fifth,  and  some  of  those  on  hissing  in  the  tenth,  also 
belonged  to  this  Chicago  Paper,  which  was  as  full  of 
suggestion  as  it  was  rich  in  accomplished  work. 

Although  the  book  is  concerned  entirely  with  the  arc 
itself,  and  does  not  touch  at  all  upon  lamps  and  their 
devices,  it  is  hoped  that  it  may  appeal  to  the  practical 
man  as  well  as  to  the  physicist.  For  not  only  the 
cause  but  the  practical  bearing  of  each  peculiarity  of 
the  arc  has  been  considered  ;  the  directions  in  which 
improvements  may  be  hoped  for  have  been  pointed  out, 


PREFACE.  vii. 

and  the  conditions  requisite  to  secure  the  maximum 
production  of  light  from  a  given  expenditure  of  power 
in  the  generator  have  been  fully  discussed. 

In  conclusion,  I  have  to  thank  Prof.  Blondel,  Prof. 
Fleming  and  Mr.  Trotter  for  kind  permission  to  use 
figures  from  their  Papers ;  Mr.  Fithian  for  taking  the 
beautiful  photographs  of  the  Hissing  Arc  reproduced 
in  Fig.  8 1  ;  Mr.  Mather  for  much  valuable  advice  and 
assistance  with  experiments,  and  Mr.  Maurice  Solomon 
for  his  suggestive  criticism  of  the  MS.  and  careful 
revision  of  the  proofs. 

HERTHA   AYRTON. 


TABLE  OF  CONTENTS. 


CHAPTER  I. 

PAGE 

THE  APPEARANCE  OF  THE  ARC   1 

Colours  of  Different  Parts  of  Arc. — General  Shapes  of  Arc  and 
Carbons. — Influence  of  Current  and  Length  of  Arc  on  Shape 
and  Size  of  Arc  and  Shapes  of  Carbons. — Positive  Crater.— 
Effect  of  Core  on  Colour,  Size  and  Shape  of  Arc.— Crater  in 
Negative  Carbon. 


CHAPTER  II. 

A  SHORT  HISTORY  OF  THE  ARC 19 

Uncertainty  of  Discoverer  and  of  Date  of  Discovery  of  Arc. — 
Mutual  Attraction  between  Arc  and  Magnet. — First  Observation 
of  Crater,  "  Mushrooms,"  Smell  of  Arc,  and  Difference  of 
Temperatures  of  Electrodes. —Application  of  Laws  of  Elec- 
trolysis to  Arc. — Experiments  on  Arcs  in  Various  Gases. — 
Photographic  Power  of  Arc.  —  First  Experiments  on  Arcs 
between  Carbons  Steeped  in  Metallic  Salts.— Hissing.— Trans- 
ference of  Matter  from  One  Pole  to  the  Other. — Electric 
Blowpipe. — Water  as  One  Electrode. — Edlund's  Discovery  of 
Straight  Line  Law  of  Resistance  and  Length  of  Arc,  and 
Suggestion  of  a  Back  E.M.F.— Fall  of  P.D.  with  Hissing.— 
Internal  Pressure  of  Arc.— Measurements  of  P.D.  and  Current 
with  Constant  Lengths  of  Arc. — Measurements  of  Supposed 
True  Resistance  of  Arc. — Tests  for  Back  E.M.F. — Determinations 
of  Temperatures  of  Electrodes. — Arcs  under  Pressure. —Measure- 
ments of  Light. — Rotation. — Apparent  Negative  Resistance. — 
Attraction  of  Solid  Carbon  Particles  out  of  Arc.— Suggested 
-"Thomson  Effect"  in  Arc. — List  of  Original  Communications. 


x.  TABLE  OF  CONTENTS. 

CHAPTER  III. 

PAQE- 

11  STRIKING  "  THE  ARC  AND  SUDDEN  VARIATIONS  OF  CURRENT     97 

Impossibility  at  First  of  getting  Definite  P.D.  with  Fixed  Current 
and  Length  of  Arc. — Cause  of  Difficulty. — Low  P.D.  and 
Subsequent  Rapid  Else  on  Striking  Arc  with  Cored  Positive 
Carbon. — Influence  of  Current,  Length  of  Arc,  and  Shapes  and 
Temperatures  of  Carbons  on  Time  Required  for  P.D.  to  become 
Constant  after  Striking  Arc. — First  Rise  of  P.D.  with  Increase 
of  Current  with  Cored  Carbons. — Peculiar  Changes  of  P.D.  with 
Sudden  Changes  of  Current,  and  their  Causes. — Summary. 

CHAPTER  IV. 

CURVES  FOR  P.D.  AND  CURRENT  WITH  CONSTANT  LENGTH 
OF  ARC,  AND  FOR  P.D.  AND  LENGTH  OF  ARC  WITH 
CONSTANT  CURRENT 119* 

General  Character  of  Curves  for  P.D.  and  Current  with  Constant 
Length  of  Arc  for  Solid  Carbons. — Same  with  Positive  Carbon 
Cored. — Discussion  of  Variations  Caused  by  Core. — Different 
Positions  of  Hissing  Points  with  Solid  Carbons  and  with  Positive 
Carbon  Cored. — Influence  of  Strength  of  Current  on  Diminution 
of  P.D.  due  to  Core. — Hypothesis  as  to  Action  of  Core  in 
Modifying  P.D. — Curves  showing  Straight  Line  Law  con- 
necting P.D.  with  Length  of  Arc,  for  Constant  Current, 
with  Solid  Carbons. — Curves  for  Same  Connection  with  Cored 
Positive  Carbon,  showing  P.D.  Practically  Independent  of 
Current  for  One  Length  of  Arc. — Discussion  of  Differences 
between  the  Two  Sets  of  Curves,  and  Explanation,  on  Above- 
mentioned  Hypothesis. — Soft  and  Hard  Crater  Ratios. — Deduc- 
tions from  them  as  to  Influence  of  Current  and  Length  of  Arc 
on  Area  of  Crater. — Summary. 

CHAPTER  V. 

AREA  OF  CRATER  AND  CRATER  RATIOS. — VARIATION  OF  P.D. 
WITH  DIAMETERS  OF  CORED  CARBONS. — CONSTANT 
CURRENT-RESISTANCE  CURVES. — CONSTANT  P.D. 
CURVES 151 

Measurements  of  Diameter  of  Crater  with  Arc  Burning. — Curves 
of  Area  of  Crater  and  P.D.  between  Carbons  for  Various 
Currents  and  Lengths  of  Arc.— Curves  of  Area  of  Crater  and 
Length  of  Arc,  of  Soft  Crater  Ratio  and  Length  of  Arc,  and  of 


TABLE  OF  CONTENTS.  xi. 

Hard  Crater  Eatio  and  P.D.— Curves  of  Area  of  Crater  and 
Current.— Measurements  of  Depth  of  Crater.— P.D.  Unin- 
fluenced by  Depth  of  Crater.— Comparison  of  P.Ds.  for  Same 
Current  and  Length  of  Arc  but  Different-sized  Carbons.— 
Curves  of  Apparent  Resistance  and  Length  of  Arc.— Constant 
P.D.  Curves. — Summary. 


CHAPTER  VI. 

THE  EQUATION  FOB  P.D.,  CURRENT,  AND  LENGTH  OF  ARC, 
WITH  SOLID  CARBONS,  AND  ITS  APPLICATION  TO  THE 
RESULTS  OF  EARLIER  EXPERIMENTERS  175 

Two  Fundamental  Straight  Line  Laws  Found  to  Exist  with  Solid 
Carbons. — Power  and  Length  of  Arc  with  Constant  Current,  and 
Power  and  Current  with  Constant  Length  of  Arc. — Equation  for 
Power,  Current,  and  Length  of  Arc  found  by  Combining  these. 
— Equation  for  P.D.,  Current  and  Length  of  Arc,  Deduced  from 
it,  having  Four  Constants  Depending  Solely  on  Nature  of  Car- 
bons.—Straight  Line  Power  Laws  Shown  to  Fit  Experiments  of 
Edlund,  Frolich,  Peukert,  and  Cross  and  Shepard,  and  Equations 
for  P.D.,  Current  and  Length  of  Arc  similar  to  Above,  Deduced 
from  their  Results. — Summary. 


CHAPTER   VII. 

THE    P.D.    BETWEEN    EACH    CARBON  AND    THE    ARC,    AND    THE 

FALL  OF  POTENTIAL  THROUGH  THE  ARC  207 

Repulsion  and  Attraction  of  Arc,  and  other  Disturbances  caused 
by  Third  Carbon. — Definitions  of  Positive  Carbon  P.D.,  Negative 
Carbon  P.D.,  Vapour  P.O.— Variation  of  Positive  Carbon  P.D. 
with  Current  and  Length  of  Arc. — Resemblances  and  Differences 
between  Positive  Carbon  P.D.  Curves  and  Total  P.D.  Curves.— 
Variation  of  Negative  Carbon  P.D.  with  Current,  but  not  with 
Length  of  Arc. — Curves  and  Equation  for  Positive  Carbon  P.D., 
Current  and  Length  of  Arc  ;  Negative  Carbon  P.D.  and  Current ; 
and  Sum  of  Carbon  P.Ds.,  Current  and  Length  of  Arc. — Simi- 
larity between  Independent  Constant  in  the  Last  Equation  and 
Similar  Constant  in  Equation  for  Total  P.D.,  Current  and  Length 
of  Arc,  Showing  that  if  this  Latter  Represents  a  Back  E.M.F.,  it 
must  be  Located  at  Junctions  of  the  Two  Carbons  with  the  Arc.— 
Equation  for  Total  P.D.,  Current  and  Length  of  Arc  with  Third 
Carbon  in  Arc. — Location  of  P.Ds.  Represented  by  Three  out  of 


xii.  TABLE  OF  CONTENTS. 

Four  Terms  of  Equation  for  Total  P.D.,  Current  and  Length  of 
Arc.— Measurements  of  Carbon  P.Ds.,  Plus  Vapour  P.D.— Car- 
bon and  Vapour  P.Ds.  with  Cored  Carbons. — Diminution  of  P.D. 
due  to  Core  Traced  to  Junction  of  Positive  Carbon  and  Arc,  and 
to  Lowering  of  Resistance  of  Vapour  Column. — Summary. 


CHAPTER  VIII. 

RELATIONS  BETWEEN  E.M.F.  OF  GENERATOR,  RESISTANCE 
IN  SERIES  WITH  ARC,  P.D.,  CURRENT  AND  LENGTH  OF 
ARC  WITH  SOLID  CARBONS  —  241 

Graphical  Method  of  Finding  Relations  between  E.M.F.  of  Gene- 
rator, Resistance  in  Series  with  Arc,  P.D.,  Current  and  Length  of 
Arc. — Impossibility  of  Keeping  either  Current  or  Length  of  Arc 
really  Constant. — Greatest  Length  of  Arc  possible  with  Given 
Resistance  in  Series. — Reason  for  Difficulty  frequently  found  in 
Maintaining  Long  Arcs  with  Small  Currents.  —  Necessity  of 
"Steadying  Resistance"  in  order  that  Silent  Arc  may  be 
Maintained  at  all.— Variation  of  Minimum  Value  of  Steadying 
Resistance  with  Current  and  Length  of  Arc. — Longest  Silent 
Arc  and  Smallest  Current  that  can  be  Maintained  with  Given 
E.M.F.  and  Resistance  in  Series  with  Arc.— Largest  Resistance 
and  Smallest  Current  that  can  be  Used  with  Given  E.M.F.  and 
Length  of  Arc. — Largest  Resistance  and  Longest  Arc  that  can 
be  Maintained  with  given  E.M.F.  and  Current. — Summary. 


CHAPTER   IX. 

THE  POWER  EFFICIENCY  OF  THE  ARC  AND  THE  RESISTANCE 

NEEDED  IN  SERIES  WITH  IT  • 259 

General  Conditions  for  Ratio  of  Power  Expended  in  Arc  to  Power 
Developed  by  Generator  (Power  Efficiency)  to  be  Greatest  Pos- 
sible.—Conditions  for  Power  Efficiency  to  be  Greatest  Possible 
(1)  when  Length  of  Arc  alone  is  Fixed,  (2)  when  E.M.F.  alone 
is  Fixed,  (3)  when  Current  alone  is  Fixed,  (4)  when  Resistance 
in  Series  alone  is  Fixed,  (5)  when  P.D.  alone  is  Fixed. — Minimum 
Resistance  that  can  be  used  in  Series  with  Arc  varies  Inversely  as 
Square  of  Current  for  Fixed  Length  of  Arc.— Minimum  Resis- 
tance Required  to  Maintain  Silent  Arc  at  all  Depends  only  on 
Nature  of  Carbons. — Summary. 


TABLE  OF  CONTENTS.  xiii. 

CHAPTER  X. 

HISSING  ARCS 277 

Variety  of  Hissing  Sounds.— Hissing  Arc  not  necessarily  Short.— 
Instability  of  Arc  about  Hissing  Point.— Laws  of  Hissing  from 
P.D.-Current  Curves.— Cross  and  Shepard's  and  Luggin's 
Experiments.— Equation  to  Curve  on  which  Hissing  Points  Lie.— 
Largest  Current  with  which  Arc,  however  long,  can  Remain 
Silent— Equation  for  P.D.  and  Length  of  Arc  with  Hissing.— 
Fall  of  P.D.  at  Positive  Carbon,  and  Diminution  of  Resistance  of 
Arc,  with  Hissing.— Equation  Connecting  Change  of  P.D.  when 
Hissing  Begins  with  Length  of  Arc.— Smallest  Hissing  Current 
\*ith  given  Length  of  Arc.— Connection  between  Largest  Silent 
and  Smallest  Hissing  Current  of  same  Arc. — Change  in  Appear - 
anue  of  Crater,  Arc,  and  Carbons  with  Hissing.—  Crater  more  than 
Covering  End  of  Positive  Carbon  with  Hissing. — Laws  of  Hissing 
Deduced  from  Shapes  of  Positive  Carbons  with  various  Currents. — 
Cause  of  Hissing. — Experiments  on  Arcs  enclosed  in  Crucible. — 
Blowing  Various  Gases  against  Crater. — Different  Behavour  of 
Arc  when  Hydrogen  is  Blown  against  Crater  in  Open  Air  and  in 
Crucible. — Cause  of  Hissing  Sound. — Summary. 

CHAPTER  XL 
THE  LIGHT  AND  LUMINOUS  EFFICIENCY  OF  THE  ARC.    ...   313 

Sources  of  Light  in  Arc. — Obstruction  of  Crater  Light  by  Negative 
Carbon. — Trotter's  Theorem. — Quantity  of  Light  Obstructed  by 
Negative  Carbon  Estimated  from  Diagrams  of  Arc  and  Carbons. — 
Reason  for  Light  being  Greater  with  very  fehort  Arcs  than  with 
longer  ones,  with  Large  Currents. — Measurements  of  Mean 
Spherical  Candle- Power  of  Arc  (W.  E.  Ayrton)  and  Total  Light 
of  Arc  (Blondel)— Simultaneous*  Discovery  of  Certain  Length  of 
Arc  and  Certain  P.D.  with  which  the  Light  is  a  Maximum  for 
&  Constant  Current. — Curves  Connecting  Crater  Light  with 
Length  of  Arc,  Deduced  from  Diagrams  of  Arc  and  Carbons. — 
Distinction  between  Polar  Light  Curves,  Rousseau's  Curves,  and 
Curves  connecting  Illuminating  Power  with  Length  of  Arc. — 
Suggested  Absorption  of  Crater  Light  by  Arc. — Facts  tending 
to  show  that  Arc  does  Absorb  Light.— Experiments  on  Shadows 
•of  Candle  and  Gas  Flames. — Arc  Shadow. — Refractive  Power  of 
Arc  Mist.— Arc  Vapour  turning  in  o  Carbon  Mist.— Violet  Colour 
of  Long  Arcs  as  Proof  of  Absorption. — Light,  Length  of  Arc 
Curves,  from  Diagrams  of  Arc,  allowing  for  Absorption  of  Crater 
Light  in  Arc.— Similarity  between  these  and  Experimental 
Curves.— Effect  of  Variation  of  Current  on  Total  Light  emitted 
by  Arc.— Very  small  Luminous  Efficiency  of  all  sources  of  Light, 
Even  Arc.— Distribution  of  Power  supplied  to  Arc  between 


xiv.  TABLE  OF  CONTENTS. 

PAGE 

Carbon  Ends  and  Mist. — Waste  of  Power  in  Mist  in  Long  Arcs. — 
Conditions  for  Light  to  be  Maximum  for  given  Power  developed 
by  Generator. — Influence  of  Cross  Sections  of  Carbons  on  Light- 
ing Power. — With  Solid  Carbons  Light  Efficiency  is  greater, 
and  Arc  with  which  Maximum  Light  Efficiency  is  obtained  is 
Shorter  the  Smaller  the  Carbons. — Low  Efficiency  of  Commercial 
Arc  Lamps  due  to  Thickness  of  Carbons. — Variation  of  Light 
Efficiency  with  Current. — Effect  of  Composition  of  Carbons  on 
Light  Efficiency.— Arcs  in  Series. — Only  Fair  Method  of  Compar- 
ing Light  Efficiency  of  Two  Sources. — Summary. 

CHAPTER  XII. 

THE  MECHANISM  OF  THE  ARC — ITS  TRUE  RESISTANCE — HAS 
IT  A  LARGE  BACKE.M.F.? — THE  REASON  FOR  THE 
DIFFERENT  EFFECTS  OF  SOLID  AND  CORED  CARBONS...  391 

How  Arc  forms  on  Separating  Carbons. —  Changing  of  Vapour  into 
Carbon  Mist. — Resistivities  of  Vapour,  Mist,  and  Flame. — Source 
of  Heat  of  Arc. — Hollowing  of  Crater. — Shaping  of  Carbons. — 
Dependence  of  Area  of  Crater  on  both  Current  and  Length  of 
Arc. — Imitation  of  Back  E.M.F.  by  Vapour  Film. — Time-Change 
of  Resistance  of  Arc.  —  Effect  of  Frequency  of  an  Added  Alter- 
nating Current  on  Value  and  Sign  of  . —  Curve  of  —and 

5A  5A 

Frequency.— Frequency  with  which  —  Measures   True   Resis- 

oA 

tance  of  Arc. — Tests  for  this  Frequency. — Two  Ways  in  which 
Cores  in  Carbons  may  Affect  Resistance  of  Arc. — How  Cores 
Affect  Mean  Cross  Section  of  Mist. — How  they  Affect  Resistivity 
of  Arc  and  thus  Alter  Shapes  of  P.D.-Current  Curves. — 

Influence   of   Cores  on   Value  of — ,    (1)   in   Change  of  Cross 

oA 

Section,  (2)  in  Change  of  Specific  Resistance — Curves  Con- 
necting —  with  Current,  for  Constant  Length  of  Arc,  with 

Length  of  Arc  for  Constant  Current,  and  with  Frequency  of 
Alternating  Current,  for  both  Solid  and  Cored  Carbons. — 
Summary. 

APPENDIX.  445 

Apparent  Area  of  Disc  Viewed  from  Any  Distance.— Our  Method 
of  Estimating  Brilliancy  of  a  Source  of  Light. — Assumptions 
Made  in  Photometry. — Mean  Spherical  Candle  Power  and  Total 
Light.  —  Measurement  of  Either,  by  Means  of  Rousseau's 
Figures. — Why  Area  of  Polar  Light  Curve  Cannot  Measure 
Either. — Candle  and  Gas  Shadow  Experiments.— Supplementary 
List  of  Original  Communications. 


LIST  OF  ILLUSTRATIONS. 


FIG.  PAGE 

1  Image  of  Arc  and  Carbons,  Five  Times  Full  Size  ...  3 

2  Section  of  Positive  Carbon  Showing  Outer  Crust  Curling  Away         5 

3  Drawing  of  Arc  and  Carbons  with  both  Carbons  Solid — 4  mm. 

20  ampere  Arc      facing        6 

4  Drawing  of  Arc  and  Carbons  with  both  Carbons  Solid — 7  mm. 

20  ampere  Arc        ..         ...         ...         ...         facing        6 

5  Drawing  of   Arc  and  Carbons  with  Cored  Positive  and  Solid 

Negative  Carbon — 7  mm.  20  ampere  Arc         facing         7 

6  Drawing  of  Arc  and  Carbons  with  Cored  Positive  and  Solid 

Negative  Car- on — 18  mm.  20  ampere  Arc      facing         7 

7  Diagrams  of  Arcs  of  various  Lengths  and  with  various  Currents, 

between  18  mm.  Cored  Positive  and  15  mm.  Solid  Negative 
Carbons  (W.  E.  Ay rton) 9 

8  Diagrams  of  Arcs  of  various  Lengths  and  with  various  Currents, 

between  13  mm.  Cored  Positive  and  11  mm.  Solid  Negative 
Carbons  (W.  E.  >yrton) 10 

9  Diagrams  of  A  cs  of  various  Lengths,  anrl  with  various  Currents, 

between  9  mm.  Cored  Positive  and  8  mm.  Solid  Negative 
Carbons  (W.  E.  Ayrtou) 12 

10  Diagrams   or    Car  ons  before   and   after  Sudden  Changes   of 

Current  (W.  E.  Ayrton) 15 

11  Diagrams  of  Arcs  between  Solid  Carbons  (W.  E.  Ayrton)        ...       15 

12  Diagrams  of  Arcs  between  Solid  Positive  and  Cored  Negative 

Carbons  (W.  E.  Ayrton) 16 

13  Horizontal  Arc  copied  from  "  Davy's   Elements  of   Chemical 

Philosophy"         27 

14  Figure  shoeing  the  Rotation  of  the  Arc  at- the  Pole  of  a  Magnet       29 

15  Vertical  Parallel  Carbons  showing  the  Position  the  Arc  takes 

up  near  the  end-  (W.  E.  Ayrton)          ...         36 

16  Apparatus  for  Meas-iring  the  Resistance  of  the  Arc  (Von  Lang)  43 

17  Apparatus  for  Testing  for  a  Back  E.M.F.  in  the  Arc  (Lecher) ...  52 

18  Curves  showing  Conditions  for  Arc  to  be  "Stable  (Blondel)      ...  62 

19  Apparatus  for  Testing  the  Conductivity  of  the  Arc  (Fleming)  70 


xvi.  LIST  OF  ILLUSTRATIONS. 

FIG.  PAGE. 

20  Apparatus  for  Measuring  the  Resistance  of  the  Arc  (Frith)     ...       73 

21  Apparatus  for  Measuring  the  Resistance  of  the  Arc  (Frith  and 

Rodgers) 76 

22  Curves  Connecting  the  Instantaneous  dVJdA.  with  the  Current 

for  a  Constant  P.D.  (Frith  and  Rodgers)         79 

23  Curves  Connecting  the  Instantaneous  dV/dA.  with  the  P.D.  for 

a  Constant  Current  (Frith  and  Rodgers)         ...         ...         ...       80 

24  Apparatus  for  Measuring  the  Back  E.M.F.  of  the  Arc  (Arons)...       82 

25  Illustration  of  Experiments  on  Particles  Shot  out  from  Carbons 

(Herzfeld) 85 

26  Apparatus  for  Testing  for  a  Back  E.M.F.  in  the  Arc  (Blondel)  88 

27  Apparatus  for  Testing  for  a  B*ck  E.M.F.  in  the  Arc  (Granquist)  '  92 

28  Hand  Fed  Arc  Lamp          98 

29  Plan   of  Arc   Lamps,    Lens,  Mirror  an  I  Diagram  Screen  for 

Magnifying  the  Image  of  the  Arc         ...         ...          ...         ...       99 

30  P.D.  and  Current  Curves  drawn  before  the  Time- Variability  of 

the  P.D.  was  Realised  (W.  E.  Ayrton) 101 

31  Curves  for  Time-Change  of  P.D.  with  Constant  Current  and 

Length,  after  starting  the  Arc  between  Cored  Positive  and 
Solid  Negative  Carbons  (W.  E.  Ayrton)  103 

32  Curves  for  Time-Change  of  P.D.  with  Constant  Current  and 

Length,  after  starting  the  Arc  between  Carbons  of  various 
kinds,  with  ends  variously  shaped  (W.  E.  Ayrton)      ...         ...     105 

33  The  same  (W.  E.  Ayrton) 107 

34  Curves  showing  the  Influence  of  the  Shape  of  the  Negative 

Carbon  on  the  Time-Change  of  P.D.  (W.  E.  Ayrton)  ..         ...     109 

35  Curves  for  Time- Change  of  P.D.  with  Solid  and  Cored,  Flat  and 

Normal,  and  Hot  and  Cold  Carbons  (W.  E.  Ayrton) 110 

36  Curves  for  Time-Change  of  P.D.  with  Sudden  Changes  of  Current, 

showing   the   Influence   of  a  Core  in-  the  Positive  Carbon 

(W.  E.  Ayrton) „         ...     113 

37  Curves  for  Time-Change  of  P.D.  with  Sudden  Changes  of  Current, 

Showing  the  Influence  of  the  Length  of  the  Arc  (W.  E.  Ayrton)     114 

38  Curves   connecting   the    P.D.   with   the   Current  for  various 

Constant  Lengths  of  Arc,  with  Solid  Carbons  ...         ...     120 

39  The  same,  with  18  mm.  Cored  and  15  mm.  Solid  Carbons  (W.  E. 

Ayrton)      128 

40  The  same  with  13  mm.  Cored  and  11  mm.  Solid  Carbons  (W.  E. 

Ayrton)      129 

41  The  same  with  9  mm.  Cored  and  8  mm.  Solid  Carbons  (W.  E. 

Ayrton)     130 

42  Curves  showing  the  Changes  in  the  P.D.  produced  by  Coring 

the  Positive  Carbon  (W.  E.  Ayrton) 132 

43  Hypothetical   Curves   of   P.D.   and    Current,  for   a    Constant  « 

Length  of  Arc,  showing  the  Effect  of  Coring  the  Positive 
Carbon      ,     134 

44  Cui  ves  connecting  P.D.  and  Length  of  Arc  for  various  Constant 

Currents.     Solid  Carbons  136 


LIST  OF  ILLUSTRATIONS.  Xvii. 

FIG*  PAQB 

45  The   same  with   18   mm.   Cored  and  15  mm.  Solid  Carbons 

(W.  E.  Ayrbon) „.         ...     139 

46  The  same  with  13  mm.   Cored  and  11  mm.  Solid   Carbons 

(W.  E.  Ayrton) 140 

47  The   same   with    9    mm.    Cored    and    8    mm.    Solid   Carbons 

(W.  E.  Ayrton) 140 

48  The  same  with  both  Carbons  Cored  (W.  E.  Ayrton)      142 

49  Hypothetical  Curves  of  P.D.  and  Length  of  Arc,  for  a  Con- 

stant Current,  showing  the  Effect   of   Coring  the  Positive 
Carbon      ...         ...         ...  ..         ...         144 

50  Curves  connecting  the  Area  of  the  Crater  with  the  P.D.  between 

the  Carbons,  for  various  Constant  Currents 153 

51  Curves  connecting  the  Area  of  the  Crater  with  the  Length  of 

the  Arc,  for  various  Constant  Currents  155 

52  Curves  connecting  the  Soft  Crater  Ratio  with  the  Length  of  the 

Arc,  for  various  Constant  Currents      ...         ...         156 

53  Curves  connecting  the  Hard  Crater  Ratio  with  the  P.D.  between 

the  Carbons,  for  various  Constant  Currents 157 

54  Curves  connecting  the  Area  of  the  Crater  with  the  Current,  for 

various  Constant  Lengths  of  Arc          ...         ...     159 

55  Curves  connecting  the   P.D.   between  the  Carbons  with  the 

Length  of  the  Arc,  for  Cored  Positive  and  Solid  Negative 
Carbons  of  various  Diameters    ...         ...         163 

56  Curves  connecting  the  Apparent  Resistance  of  the  Arc  with  its 

Length,  for  various  Constant  Currents,  with  18  mm.  Cored 

and  15  mm.  Solid  Carbons         ...         ...         164 

57  The  same  with  13  mm.  Cored  and  11  mm.  Solid  Carbons        ...     165 

58  The  same  with  9  mm.  Cored  and  8  mm.  Solid  Carbons  ...     166 

59  Curves   connecting  Current   with  Length   of  Arc  for  various 

Constant  P.Ds 169 

60  Curve  connecting  Current  with  Time  for  a  Constant  P.D.  and 

Length  of  Arc      171 

61  Curves  connecting  P.D.   with    Current,  for  various  Constant 

Lengths  of  Arc,  with  Solid  Carbons 177 

62  Curves  connecting  Power  expended  in  Arc  with  Length  of  Arc, 

for  various  Constant  Currents,  with  Solid  Carbons 180 

63  Curves  connecting  Power  with  Current,  for  Lengths  of  Arc  0  mm. 

and  7  mm.,  with  Solid  Carbons 182 

64  Hyperbola  connecting  P.D.  with  Current,  for  a  Constant  Length 

of  Arc,  with  Solid  Carbons         187 

65  Curves   connecting   Power   with   Length   of  Arc,  for   various 

Constant  Currents,  from  Peukert's  Experiments      194 

66  Curves  connecting  Power  with  Current,  for  Lengths  of  Arc  0  mm. 

and  10  mm.,  from  Peukert's  Experiments      196 

67  Curves   connecting   Power  with   Length   of   Arc  for   various 

Constant  Currents,  from  Cross  and  Shepard's  Experiments...     199 

68  Curves  connecting  Power  with  Current  for  Lengths  of  Arc  0 

and  ^§  inch,  from  Cross  and  Shepard's  Experiments 200' 


xviii.  LIST  OF  ILLUSTRATIONS. 

FIG.  PAGE 

69  Diagrammatic  Representation  of  Apparatus  used  for  Finding 

the  P.D.  between  each  Carbon  and  the"  Arc 209 

70  Diagrammatic    Representation    of    various    Arrangements    of 

Main  and  Exploring  Carbons     ...         ....         ...         ...         .«     213 

71  Curves   connecting    Positive-Carbon    P.D.  with    Current,  for 

various  Constant  Lengths  of  Arc          ...         ...         ...         ...     215 

72  Curves  connecting  Positive- Carbon  P.D.  with  Length  of  Arc,  for 

various  Constant  Currents         ...         ...         ...         ...         ...     216 

73  Curves  connecting  Negative- Carbon   P.D.   with  Current,  for 

various  Constant  Lengths  of  Arc          ...         ...         ...         ...     218 

74  Curves  connecting  Negative-Carbon  P.D.  with  Length  of  Arc,  for 

various  Constant  Currents         ...         ...         ...         ...         ...     219 

75  Curves  connecting  Positive- Carbon  Power  with  Length  of  Arc, 

for  various  Constant  Currents...         ...         ...         ...         ...     220 

76  Curves  connecting  Positive- Carbon   Power  with  Current,  for 

various  Constant  Lengths  of  Arc          ...         ...         ...         ...     221 

77  Curve  connecting  Negative- Carbon  Power  with  Current  for  any 

Length  of  Arc 224 

78  Curves  connecting  Positive-Carbon  P.D.  plus  Negative  Carbon 

P.D.  with  Current,  for  various  Constant  Lengths  of  Arc      ..     226 

79  Curves  used  for  determining  graphically  the  Relations  between 

the  E.M.F.  of  the  Dynamo,  the  outside  Resistance  in  the 
Circuit,  the  P.D.,  Current,  and  Length  of  Arc  with  Solid 
Carbons 242 

80  Curves  connecting  P.D.   with    Current,  for  various  Constant 

Lengths  of  Arc,  with  Solid  Carbons     ...         ...         ...         ...     280 

81  Photographs  of  Arcs — immediately  after   Hissing  has  begun, 

after  Hissing  has  continued  so  me  time,  and  when  the  Arc  has 
become  Silent  again  ...  ...  .„  ...  ...facing  292 

82  Diagram  of  a  Short  Hissing  Arc  ...         ...         ...         ...         ...     293 

83  Diagrams  of  a  Silent  and  a  Hissing  Arc  ...         .„         ...         ...     294 

84  Diagrams  of  Arcs  and  Carbons  with  Current  increasing  from 

6  amperes,  silent,  to  30  amperes,  hissing         ...         ...         ...     295 

85  Diagrams  of  Arcs  and  Carbons  with  the  same  Current  and 

Length  of  Arc,  but  different  sized  Carbons     ...         ...         ...     296 

86  Crucible  Employed  for  Experiments  on  Enclosed  Arcs  ...     302 

87  Curves  connecting  P.D.  with  Current  for  a  nearly  Constant 

Length  of  Arc  when  the  Arc  was  enclosed  in  a  Crucible      . . .  304 

88  Disc  Viewed  from  a  Distance        317 

89  Tracings  of  "  Normal"  Arc  (Trotter)      ...         318 

90  Tracings  of  Short  Arc  (Trotter) 319' 

91  Polar  Curves  of  Apparent  Area  of  Crater  and  Candle  Power  in 

"  Normal"  Arc  (Trotter)  320 

92  Polar  Curves  of  Apparent  Area  of  Crater  and  Candle  Power  in 

Short  Arc  (Trotter)         321 

93  Curve  connecting  Apparent    Area   of   Crater  with  Light  of 

"Normal"  Arc  (Trotter)  322 


LIST  OF  ILLUSTRATIONS.  xix. 

FIG.  PAGE 

94  Diagrams  of  Arcs  and  Carbons  for  showing  the  Variation  in  the 

Shape  of  the  Negative  Carbon  with  the  same  Current  but 
different  Lengths  of  Arc...         ...         ...         ...     324 

95  Side  View  of  Apparatus  used  in  Measuring  the  Mean  Spherical 

Candle  Power  of  the  Arc  (W.  E.  Ay rton)       326 

96  General  Plan  of  Apparatus  for  Measuring  the  Mean  Spherical 

Candle  Power  of  the  Arc  (W.  E.  Ayrton)       327 

97  Curves  connecting  Mean  Spherical  Candle  Power  with  Length 

of  Arc,  for  various  Constant  Currents  (W.  E.  Ayrton)         ...     329 

98  Curves  connecting  Total  Light  emitted  with  Length  of  Arc  for 

a  Constant  Current         ...         ...         ...         ...         ...         ...     330 

99^  Apparatus  employed  in  Measuring  the  Total  Light  emitted  by 

100  J      the  Arc  (Blondel)  331 

101  Curves   connecting   Total   Light  with   Length   of   Arc    for  a 

Constant  Current  with  Solid  Carbons  of  various  sizes  (Blondel)     333 

102  Curves  connecting  Total  Light  with  Length  of  Arc,  for  a  Constant 

Current,  with  Cored  Positive  and  Solid  Negative  Carbons  of 
various  Sizes  (Blondel)    ...         ...         ...         ...         334 

103  Diagrams  of  Arcs  of  different  Lengths,  with  the  same  Current, 

between  the  same  Carbons        ...         ...         ...         336 

104  Area  proportional  to  Total  Light  that  would  be  received  from  the 

Crater  if  none  were  obstructed  by  the  Negative  Carbon      . . .     338 

105  Area  proportional  to  Total  Light  actually  received  from  Crater    339 

106  Diagram  of  Arc  and  Carbons  with  Lines  for  finding  the  Quantity 

of   Light    Obscured   by  the    Negative  Carbon    in    any  one 
direction   ...         ...         ...         ...         ...         ...         ...         ...     340 

107  Geometrical  Construction  for  the  Area  of  Crater  Obscured  by 

the  Negative  Carbon  in  any  one  direction       ...         ...         ...     341 

108  Curves  connecting  Light  received  from  Crater  with  Length  of 

Arc,  obtained  from  Diagrams  in  Fig.  103        ...         343 

109  Photograph  of  Candle  Flame        350 

110  Section  of  Apparatus  used  for  Observing  the  Shadow  of  the 

Arc 353 

111  The  Light  from  the  Crater,  the  Arc  Mist,  and  the  White  Spot, 

passing  through  a  narrow  Slit  on  to  a  White  Screen 358 

112  Band  of  Violet  Light,  bordering  a  Shadow  made  by  intercepting 

the  Light  of  the  Crater  of  an  Arc         ...  359 

113  Arc  with  Mist  divided  into  Layers  of  Equal  Thickness  ...     361 

114  Hypothetical  Curves  obtained  from  Fig.  108  by  allowing  for 

the  Absorption  of  Crater  Light  by  the  Arc  Mist        363 

115  Diagrams   of    Arc   and  Carbons,  showing   the   Effect   on   the 

Shapes  of  both  Carbons   of    varying   the   Current   with   a 
Constant  Length  of  Arc 365 

116  Curves  connecting  the  Mean  Spherical  Candle  Power  of  the 

Arc  with  the  Current,  for  Constant  Lengths  of  Arc  of  1  mm. 
and  4  mm.  (W.  E.  Ayrton)       366 

117  Curves  connecting  the  Total  Light  emitted  by  the  Arc  with  the 

Current,  for  a  Constant  P,D.  of  45  volts  (Blondel)    367 


xx.  LIST  OF  ILLUSTRATIONS. 

FIG.  PAGE 

118  Curves  connecting   the   Power   supplied  to  the  Arc  and  the 

Power  absorbed  by  the  Mist  with  the  Length  of  the  Arc,  for 

a  Constant  Current  of  10  amperes        ...         ...         ...         ...     373 

119  Curve  showing  the  proportion  of  the  whole  Power  supplied  to 

the  Arc  that  is  Wasted  in  the  Mist,  with  a  Constant  Current 

of  10  amperes       ...         ...         ...         ...         ...         ...         ...     373 

120  Diagrams  of   Arc   and   Carbons  with    the  same  Current  and 

Length  of  Arc,  but  different  sized  Carbons     ...         ...         ...     376 

121  The  same      379 

122  Curves  connecting  Light  Efficiency  with  Length  of  Arc  for  a 

Constant  Current  of  10  amperes  with  Solid  Carbons  (Blondel)     381 

123  The  same   with  Cored  Positive  and   Solid  Negative  Carbons 

(Blondel)  382 

124  Curves  connecting  Light  Efficiency  with  Length  of  Arc  for  a 

Constant  P.D.  (Blondel) 385 

125  The  Shaping  of  the  Negative  Carbon  with  Large  and  Small 

Craters  and  with  Long  and  Short  Arcs  ...         ...         ...     395 

126  Hypothetical  Areas  of  Volatilisation  and  Non-volatilisation  in 

Crater        397 

127  Shapes  assumed  by  the  Positive  Carbon,  with  the  same  Area 

of  Volatilisation,  but  with  a  Long  Arc  in  the  one  Case  and  a 
Short  Arc  in  the  other 398 

128  Diagrams  of  Arc  and  Carbons  with  Mist  and  Flame  very  care- 

fully Outlined      401 

129  Curve  counecting  the  Power  Expended  in  the  Arc  Mist  with 

the  Current,  for  a  Constant  Length  of  Arc  of  2  mm.  . .     403 

130  Curves  showing  Simultaneous  Time-Changes  of  P.D.,  Current 

and  Eesistance 405 

131  Curves  showing  the  Effect  of  the  Frequency  of  an  Alternating 

Current,  Superimposed  on   a  Direct   Current  Arc,  on  the 
Simultaneous  Time-Changes  of  P.D.  and  Current     408 

132  Curves  connecting  Values  of—   with  the  Frequency   of   the 

Superimposed  Alternating  Current      ...         ...         ...         ...     412 

133  Curves  connecting  the  Mean  Cross  Section  of  the   Arc  Mist 

with  the  Current,  for  a  Constant  Length  of  Arc,  with  Solid- 
Solid,  Solid-Cored,  Cored-Solid,  and  Cored-Cored  Carbons  ...     420 

134  Hypothetical  Curves  Exemplifying  the  Changes,  in  the  Curve" 

connecting  P.D.  with  Current  for  a  Constant  Length  of  Arc, 
caused  by  a  Core  in  the  Positive  Carbon         ...         ...          ...     423 

135  Hypothetical  Curves  connecting  — i  with  the  Current,  for  a 

Constant  Length  of  Arc...         ...         ...         ...         ...         ..      430 

136  Hypothetical  Curves  connecting  -— -e  with  the  Current,  for  a 

oA 
Constant  Length  of  Arc 432 

137  Hypothetical  Curves  Connecting  __    with  the  Current,  for  a 

oA 
Constant  Length  of  Arc...        ,, ,,        ,.,        ,..    434 


LIST  OF  ILLUSTRATIONS.  xxi. 

FIG.  PAGE 

138  Hypothetical  Curve  of  Time-Change  of  P.D.  Accompanying  a 

Sudden  Change  of  Current        435 

139  Hypothetical  Curves  Connecting  —  with  the  Length  of  the  Arc, 

5A 
for  a  Constant  Current    ...         ...         ...         436 

140  Hypothetical  Curves  Connecting  — with  the  Frequency  of  an 

Addei  Alteroating  Current       ...         ...         ...         ...         ...     438 

142  \  Figures  Used  in  Finding  the  Apparent  Area  of  a  Disc  ...         ...  I  ^^ 

143  |  Figures  Used  in  Finding  an  Area  Proportional  to  the  Mean  Spheri- 

144  \      cal  Candle  Power  of  an  Axially  Symmetrical  Source  of  Light     453 

145  Polar  Light  Curves  of  Two  Similar  Sources,  the  one  having 

twice  the  Illuminating  Power  of  the  other      ...         ...         ...     455 

146  Photograph  of  the  Shadow  of  a  Candle  Flame 457 


xxiii. 


LIST  OF  TABLES. 


PAGE 

I.  Current,  Resistance,  and  E.M.F.  of  Arc  (Schwendler)      ...  37 

II.  Areas  of  Crater  with  Different  Currents     ...         ...         ...  39 

III.  P.Ds.  with  Silent  and  Hissing  Arcs  (Niaudet)       40 

IV.  P.D.  Current  and  Length  of  Arc  (Nebel) 48 

V.  P.Ds.  for  Different  Conditions  of  the  Arc  (Lecher)  ...  53 

VI.  P.Ds.  with  Constant  Current  and  Varying  Lengths  of  Arc 

(Luggin) 55 

VII.  P.D.  between  Carbons  with  and  without  a  Sprinkling  of 

Soda  (Luggin)       56 

VIII.  Current   Density  and   Area  of  Tip   of   Positive  Carbon 

(Luggin)    ...         ...         ...         ...         61 

IX.  Experiments  to  Find  Back  E.M.F.  of  Arc  (Blondel)         ...     90 
X.  Experiments  to  Find  Back  E.M.F.  of  Arc  (Granquist)     ...     93 
XI.  P.D.   for    Normal     5mm.    Arc    with    Various    Constant 

Currents  (Solid  Carbons  11/9) 121 

XII.   P.D.  and  Current  with  Various  Constant  Lengths  of  Arc 

(Solid  Carbons  11/9)       122 

XIII.  Same    as    above    (Cored    Positive    and    Solid    Negative 

Carbons  18/15)  ( W.  E.  Ayrton) 125 

XIV.  Same  as  above  (Carbons  13/11)        126 

XV.  Same  as  above  (Carbons  9/8)  127 

XVI.  Diameter    of    Crater,    Square    of    Diameter,   P.D.,   and 

Current  for  Various  Lengths  of  Arc 151 

XVII.  Diameters  of  Crater,  Observed  and  Calculated,  for  Various 

Currents  and  Lengths  of  Arc    ...         ...         ...         ...  154 

XVIII.  Crater  Ratios  for  Various  Currents  and  Lengths  of  Arc  ...  156 
XIX.  Depth  of  Crater  with  Different  Currents  and  Lengths  of 

Arc  160 

XX.  Influence  of  Diameters  of  Carbons  (Positive  Cored)  on  P.D.  162 
XXI.  Comparison  of  Observed  and  Calculated  P.Ds.  for  Different 

Currents  and  Lengths  of  Arc  (Solid  Carbons  11/9)    ...  185 
XXII.  Edlund's  Results  referred  to  General  Equation  for  P.D., 

Current  and  Length  of  Arc       190 


xxiv.  LIST  OF  TABLES. 

PAGE 

XXIII.  Frolich's  Results  referred  to  General  Equation  for  P.D., 

Current,  and  Length  of  Arc          ...         ...         ...         ...  192 

XXIV.  Peukert's  Results  referred  to  the  same  Equation  ...         ...  195 

XXV.  Cross  and  Shepard's  Results  referred  to  the  same  Equation  201 

XXVI.  Duncan  Rowland  and  Todd's  Results  referred  to  the  same 

Equation 204 

XXVII.  Positive  Carbon  P.Ds.  for  Various  Currents  and  Lengths 

of  Arc  (Solid  Carbons  11/9)       214 

XXVIII.  Negative  Carbon  P.Ds.  for  Various  Currents  and  Lengths 

of  Arc  (Solid  Carbons  11/9)        217 

XXIX.  Calculated    Values    of     Positive     Carbon     P.Ds.     (Solid 

Carbons  11/9)       223 

XXX.  Calculated    Values     of     Negative    Carbon    P.Ds.    (Solid 

Carbons  11/9)       225 

XXXI.  Sum  of  Positive  and  Negative  Carbon  P.Ds.,  for  Various 

Currents  and  Lengths  of  Arc  (Solid  Carbons  11/9)   ...  227 
XXXII.  Calculated  Values    of    Sum    of    Positive   and   Negative 

Carbon  P.Ds.  (Solid  Carbons  11/9)       227 

XXXIII.  P.D.  between   Carbons  with   Third  Carbon  in  Arc  near 

Positive  Carbon  (Solid  Carbons  11/9) 229 

XXXIV.  P.D.  between  Carbons  with  Third  Carbon  in  Arc  near 

Negative  Carbon  (Solid  Carbons  11/9) ..229 

XXXV.  Mean  P.D.  between  Carbons  with  Third  Carbon  in  Arc 

(Solid  Carbons  11/9)        230 

XXXVI.  Calculated  Values  of  P.D.  between  Carbons  with  Third 

Carbon  in  Arc  (Solid  Carbons  11/9)     231 

XXXVII.  Positive   Carbon  P.D.  plus  Vapour  P.D.   (Solid  Carbons 

11/9)          ...  233 

XXXVIII.  Negative  Carbon  P.D.  plus  Vapour  P.D.  (Solid  Carbons 

11/9)          234 

XXXIX.  Comparison,  with  Solid  and  Cored  Carbons,  of  P.D.  between 

Carbons  with  Third  Carbon  in  Arc      235 

XL.  Comparison,   with  Solid  and  Cored  Carbons,  of  Positive 

Carbon  P.Ds 236 

XLI.  Comparison,  with  Solid  and  Cored  Carbons,  of  Negative 

Carbon  P.Ds 237 

XLII.  Conditions    to   obtain   Maximum   Power-Efficiency   with 
E.M.F.,  P.D.,  Current,  Length,  and  Series  Resistance 

fixed,  in  Turn  (Solid  Carbons  11/9)      270 

XLIII.  P.D.  between  Carbons  at  Hissing  Points  (Solid  Carbons 

11/9)          283 

XLIV.  Currents  at  Hissing  Points  (Solid  Carbons  11/9) 283 

XLV.  Comparison  of  Calculated  and  Observed  Values  of  P.Ds. 

at  Hissing  Points  (Solid  Carbons  11/9)  285 

XL VI.  Total  P.Ds.  and  Positive  Carbon  P.Ds.  at  Hissing  Points, 

and  with  Hissing  Arcs  (Solid  Carbons  11/9) 287 

XL VI I.  Diminution  of  Total  and  of  Positive  Carbon  P.Ds.  Accom- 
panying Hissing  (Solid  Carbons  11/9)  287 


LIST  OF  TABLES.  xxv. 

PAGE 

XLVIII.  P.D.  and  Length  of  Arc  for  Hissing  Arcs  (Cored  Positive 

and  Solid  Negative  Carbons)     ...         ...         291 

XLIX.  Effect  of  Blowing  Hydrogen  against  Crater  of  Arc  ...  306 

L.  Mean  Spherical  Candle  Power  of  Arcs  of  Different  Lengths 

with  Constant  Currents  (W.  E.  Ayrton)         328 

LI.  Crater  Light  with  and  without  Absorption  by  Arc,  for 

Arcs  of  Various  Lengths,  with  Constant  Current      .„  362 

LI  I.  Data  of  some  Commercial  Arc  Lamps         .„          383 

LIII.  Cross  Section  of  Arc  Mist,  Current,  P.D.,  and  Resistance  of, 

and  Power  Expended  in  Mist  (Solid  Carbons  11/9)  ...  402 
LIV.  Currents   and   P.Ds.    with    Small    Alternating    Current 

Superimposed  on  10  Ampere  Arc  (Solid  Carbons  11/9)  415 
LV.  Mean  Cross  Section  of  Mist  for  Different  Currents  and 

Lengths  of  Arc  with  Various  Carbons...         ...         ...  419 

LVI.  Cross  Section  of  Mist  Close  to  Crater  for  Different  Currents 

and  Lengths  of  Arc  with  Various  Carbons     ...         ...  421 

LVII.  Ratios  of  Cross  Section  of  Mist  with  one  Current  to  Cross 

Section  with  Smaller  Current ...         .,.  426 

LVIII.  Ratios  of  Cross  Section  of  Mist  Close  to  Crater  with  one 

Current  to  Cross  Section  with  Smaller  Current        ...  426 


List  of  Original  Communications  Concerning  the  Arc        ....         ...     94 

Supplementary  List      ...         m  458 


EBBATA, 


Page  13,  line  1,  for  Fig.  9  read  Fig.  7. 

Page  14,  line  3,  for  5  read  6. 

Page  50,  line  IJor  Fig.  13  read  Fig.  16. 

Page  51,  line  8  from  end,  for  back  E.M.F.  of  the  arc  read 
P.D.  between  the  carbons. 

Page  62,  line  6  from  end,  for  1890  read  1891. 

Page  64,  line  5  from  end,  for  Capt.  Abney  read  Sir  W.  de  W. 
Abney. 

Page   64,  line  3  from  end,  for  Mr.  Crookes  read   Sir.  W. 
Crookes. 

Page  88,  line  11,  for  air  read  arc. 

Page  95,  line  7  from  end,  for  p.  2  read  p.  227. 

Page  207,  line  3,  for  Twelve  read  Fourteen. 


CHAPTER   I. 


THE  APPEARANCE  OF  THE  ARC. 

SINCE  the  discovery  of  the  electric  arc  early  in  the  present 
century,  Nature  has  been  subjected  to  a  series  of  questions 
with  the  object  of  extracting  from  her  a  statement  of  the 
mysterious  laws  that  govern  it.  These  questions — which  we 
call  experiments — she  has,  so  far,  answered  but  sparingly. 
They  have  been  repeated  again  and  again,  but,  even  when 
replies  have  been  vouchsafed,  they  have  been  couched  in  such 
ambiguous  terms  that  one  experimenter  has  interpreted  them 
in  one  way,  and  another  in  another,  and  we  are  still  far 
from  having  a  clear  understanding  of  the  laws  of  the  arc. 

A  certain  amount  of  knowledge  has,  however,  been  gained, 
and  it  is  proposed  in  the  present  work  to  deal  with  some  of 
the  facts  that  have  been  acquired  concerning  direct-current 
arcs,  maintained  between  carbon  rods,  the  arc  being  not  longer 
than  the  diameter  of  the  positive  carbon,  and  the  potential 
difference  between  the  rods  being  not  greater  than,  say,  100 
volts.  It  is  proposed,  in  fact,  to  deal  only  with  such  direct- 
current  arcs  as  are  used  in  the  lighting  of  our  streets,  and  to 
leave  on  one  side  alternate-current  arcs,  very  long  arcs  main- 
tained with  a  large  potential  difference  between  the  carbons, 
and  arcs  maintained  between  metals. 

The  arc  is  so  bright  that,  if  looked  at  with  the  naked  eye, 
it  appears  to  be  simply  a  dazzlingly  bright  spot  with  needle-like 
rays  diverging  from  it  in  all  directions,  but  by  projecting  its 
image  on  to  a  screen  its  real  shape  and  colour  may  be  easily 
observed — if  the  image  is  magnified,  so  much  the  better. 

In  arcs  maintained  between  vertical  carbon  rods,  with  the 
positive  carbon  uppermost,  both  shape  and  colour  vary  accord- 
ing to  the  length  of  the  arc  and  the  current  flowing,  but 
certain  characteristics  are  common  to  all.  In  all,  the  end  of 

A 


2  THE  ELECTRIC  ARC. 

the  positive  carbon  is  more  or  less  pointed,  with  a  depression 
at  the  tip  called  the  crater.  This  depression  is  shallower,  the 
longer  the  arc,  and  is  practically  non-existent  with  arcs  of 
lengths  approaching  the  diameter  of  the  positive  carbon. 

The  end  of  the  negative  carbon  is  also  pointed,  but  instead 
of  a  depression  it  often  has  a  sort  of  little  hillock  on  the  tip. 
The  tips  of  both  carbons  are  white  hot,  and  in  the  space 
between  them  there  is  a  faint  purple  light,  outlined  by  a  deep 
shadow. 

At  a  very  early  stage  in  the  experiments  made  by  the 
students  of  the  Central  Technical  College,  under  Prof.  Ayrton's 
direction,  it  was  found  that  altering  either  the  current  or  the 
length  of  the  arc  caused  a  change  in  the  shapes  of  the  carbons 
and  visible  arc,  which  in  some  cases  was  very  considerable. 
It  was  therefore  thought  advisable  to  obtain  a  record  of  these 
changes  under  all  circumstances,  and  diagrams  of  the  carbons 
and  arc  were  taken,  when  the  potential  difference  had  acquired 
its  steady  value,  for  all  the  currents  and  lengths  of  arc  observed. 

The  diagrams  were  obtained  by  placing  a  piece  of  squared 
paper  over  the  screen  on  which  the  enlarged  image  of  the  arc 
was  projected,  and  drawing  the  complete  outlines  of  the  carbons 
and  image.  The  carbons  are  always  easy  enough  to  draw 
for  they  are  very  definite,  but  the  exact  curve  which  outlines  the 
purple  image  of  the  arc  is  much  more  difficult  to  obtain,  for  this 
image  melts  off  very  gradually  into  the  surrounding  darkness. 

Fig.  1  is  a  reproduction  of  one  of  the  diagrams  half  of 
the  original  size,  and  since  the  original  diagram  enlarged  the 
carbons  ten  times,  this  reproduction  shows  them  Jive  times  full 
size  It  may  be  observed  that  there  is  a  white-hot  crater  at 
the  end  of  the  positive  carbon,  and  a  white-hot  tip  to  the 
negative,  and  that  the  area  of  the  crater  in  the  positive  is 
much  larger  than  the  area  of  the  white-hot  tip  of  the 
negative.  That  this  glowing  tip  of  the  negative  carbon  gives 
out  a  fair  amount  of  light  may  be  easily  seen  by  observing  the 
beam  of  light  from  an  arc  after  it  has  passed  through  a  lens. 
This  beam  divides  itself  into  two  distinct  parts,  separated  by  a 
dark  space,  so  that  it  looks  like  two  beams,  one  coming  from 
the  crater  of  the  positive,  the  other  from  the  bright  spot 
on  the  negative  carbon.  If  a  piece  of  paper  be  placed  in  the 
dark  space  between  the  two  beams,  it  will  have  a  faint  violet 


Dull 


Ydllo 


Dar 


Sh 


Vihit 


Vic  let 


Red. 


Y'llow 


\ 


: 


ts. 


FIG.  1.— Image  of  Carbons  and  Arc  5  times  full  size.    Current,  10  amperes. 
Length  of  Arc,  3mm.    P.O.  steady  at  46 -5  volts. 


4  THE  ELECTRIC  ARC. 

light  on  it,  but  this  light  is  evidently  not  sufficient  to  make  the 
dust  particles  in  the  air  visible. 

The  area  of  the  bright  spot  on  the  tip  of  the  negative  carbon 
increases  with  the  current,  but  at  a  much  slower  rate  than  the 
area  of  the  crater  in  the  positive,  so  that  the  ratio  of  the  area 
of  the  crater  to  the  area  of  the  negative  bright  spot  increases 
rapidly  as  the  current  is  increased,  with  silent  arcs. 

The  part  marked  "bright  spots"  on  the  negative  carbon 
represents  a  circlet  of  seething  balls,  which,  whatever  they 
may  be,  always  appear  at  the  junction  of  the  light  and  dark 
parts  of  the  negative  carbon.  Above  them,  as  far  as  the 
line  which  is  marked  "  yellow,"  the  carbon  presents  a  granu- 
lated appearance,  being  covered  with  very  small  boiling 
balls,  and  the  whole  being  of  a  reddish  yellow  colour.  Then 
comes  the  yellow-hot  part,  marked  "  yellow,"  which  is  quite 
smooth,  and  finally  the  white-hot  tip. 

The  positive  carbon  has  also  its  smooth  yellow-hot  part  marked 
"  yellow,"  and  its  band  of  granulated  darker  yellow  part  above 
that,  and  higher  still  its  circlet  of  seething  balls — larger  than 
those  on  the  negative.  The  outlines  of  these  balls  are  indicated 
(Fig.  1)  in  the  highest  wavy  line,  but  they  cannot  generally  be 
seen  very  distinctly,  because  no  light  is  thrown  on  to  them  to  be 
reflected  back  again,  in  the  same  way  as  the  light  from  the 
crater  is  cast  on  to  the  negative  carbon. 

Looking  at  the  arc  itself  through  smoked  glass,  instead  of 
at  the  image,  it  is  seen  that  these  balls  are  really  the 
frayed  ends  of  an  outer  crust  of  the  carbon  which  is 
peeling  off.  It  is  as  if  the  inner  part  of  the  carbon,  being 
much  hotter  than  this  outer  crust,  caused  it  to  expand 
and  split,  forming  a  sort  of  fringe  hanging  down  over  the  inner 
hotter  part  from  which  it  has  broken  away.  Between  this 
crust — which  crumbles  at  a  touch  when  cold — and  the  body  of 
the  carbon  there  is  a  space  of  from  Jmm.  to  1mm.  to  the  height 
of  5mm.  or  more,  from  which  when  the  arc  is  burning  sparks 
fly  out,  drop  down  to  the  edge  of  the  crust,  and  then  fly  out- 
wards and  upwards,  probably  carried  along  by  the  strong 
upward  draught  of  the  column  of  hot  carbon  and  air.  It  is 
possible  that  they  finally  settle  on  the  positive  carbon,  for 
after  the  arc  is  extinguished  this  carbon  is  found  to  have 
numerous  small  particles  of  carbon  on  it  arranged  fairly 


THE  APPEARANCE  OF  THE  ARC.  5 

symmetrically.  The  tips  of  the  strips  of  carbon  that  form 
the  outer  crust  apparently  get  burnt  by  the  hot  volatile  carbon 
into  a  semi-globular  shape,  and  they  boil  and  bubble  under  the 
action  of  this  heat  just  as  a  lump  of  sugar  does  when  held  in  a 
candle  flame,  and  probably  the  action  is  really  very  much  the 
same  in  both  cases. 

Fig.  2  is  a  drawing  of  a  section  of  a  positive  carbon  with 
its  outer  crust,  A,  showing  the  way  in  which  this  outer  crust 
bulges  out  and  leaves  a  space  between  itself  and  the  inner  part 
of  the  carbon,  B. 


FIG.  2.  — Section  of  Positive  Carbon  with  the  Outer  Crust  curling  away 

from  it. 

Between  the  part  of  the  arc  marked  "  violet "  in  Fig.  1  and 
that  marked  "green"  there  is  a  dark  space,  which  is  scarcely 
perceptible  with  small  currents  and  short  arcs,  but  becomes 
very  wide  and  well  marked  with  large  currents  and  long  arcs. 
The  "  green  "  line  shows  the  extreme  edge  of  the  luminous  part 
of  the  arc,  or,  at  least,  of  that  part  which  is  bright  enough  to 
show  light  on  the  image. 

Figs.  3  to  6  show  clearly  the  outlines  of  the  purple  and  green 
parts  of  the  arc,  and  of  the  shadow  between  them,  under 
different  conditions. 

These  figures  I  obtained  by  tracing  the  enlarged  outlines 
of  the  carbons  and  arc  in  the  way  already  described;  very 


6  THE  ELECTRIC  AEG. 

special  attention  being  given  to  the  outlines  of  the  purple  part 
of  the  arc,  the  shadow,  and  the  green  outside  part.  The 
outlines  were  then  shaded,  so  as  to  give  as  nearly  as  possible 
the  values  of  the  light  given  out  by  each  part.  Thus  the  most 
light  is  given  out  by  the  crater  of  the  positive  carbon, 
and  by  the  tip  of  the  negative  carbon ;  therefore  these  were 
left  white.  The  shadows  between  the  purple  and  green  parts 
of  the  arc  are  somewhat  more  abrupt  than  they  really  were, 
but  their  shapes  are,  I  believe,  correct.  Unless  the  axes  of  the 
two  carbons  are  absolutely  in  line,  the  arc  is  always  a  little  to 
one  side  or  the  other,  and  that  is  the  reason  that  the  arc  in 
all  these  four  figures  is  slightly  out  of  the  centre  ;  it  is  almost 
impossible  to  get  it  perfectly  central. 

In  Fig.  4  the  outlines  of  the  balls  of  boiling  carbon  on  the 
positive  as  well  as  on  the  negative  carbon  are  shown.  In  Figs. 
3  and  5  they  could  only  be  seen  on  the  negative  carbon,  and 
in  Fig.  6  the  arc  was  so  long  that  the  screen  was  not  large 
enough  to  show  the  boiling  balls  on  either  of  the  carbons. 

The  current  used  for  the  whole  four  figures  was  20  amperes, 
the  carbons  were  18mm.  positive  and  15mm.  negative. 

In  Fig.  3  the  length  of  arc  was  4mm.,  and  the  carbons  used 
were  both  solid.  It  may  be  seen  that  the  central  purple  part 
of  the  arc  is  of  the  form  of  an  oblate  spheroid,  broken  in  upon 
by  the  tips  of  the  carbons.  Another  diagram,  made  at  the  same 
time,  of  an  arc  of  the  same  length  and  with  the  same  current,  but 
with  the  positive  carbon  cored,  showed  a  central  part  of  much 
the  same  shape,  but  of  smaller  area,  smaller,  in  fact,  not  only  in 
width,  but  in  length,  because  although  the  distance  between  the 
tip  of  the  negative  carbon  and  the  plane  through  the  edge  of  the 
crater  was  in  each  case  4mm.,  the  central  part  surrounded  a 
much  greater  length  of  the  point  of  the  negative  with  the 
solid  positive  carbon  than  with  the  cored.  The  green  part  of 
the  arc  also  started  much  higher  up  the  negative  with  the 
cored  than  with  the  solid  positive  carbon,  and  touched  the 
positive  carbon  4mm.  from  its  tip,  whereas  the  green  part 
could  be  seen  at  a  distance  of  14'5mm.  up  the  solid  positive 
carbon  (Fig.  3).  Thus,  the  whole  visible  part  of  the  arc  is 
much  larger  with  a  solid  than  with  a  cored  positive  carbon  with 
an  arc  of  4mm.  and  a  current  of  20  amperes,  but  the  general 
form  of  the  arc  is  very  much  the  same. 


FIG.  3.— Carbons  :  Positive,  18mm.  solid  ;  Negative,  15mm.  solid.    Current,  20  amperes. 
P.D.  between  Carbons,  48  volts.    Length  of  Arc,  4mm 


?•'  i 


/ 


FIG.  4.- Carbons  :  Positive,  18mm.  solid  ;  Negative,  15mm.  solid.    Current,  20  amperes. 
P.D.  between  Carbons,  r>G  volts.     Length  of  Arc,  7mm. 


FIG.  5.— Carbons  :  Positive,  18mra.  cored  ;  Negative,  15mm.  solid.    Current,  20  amperes. 
P.D.  between  Carbons,  51  volts.    Length  of  Arc,  7mm. 


4 


FIG.  6.— Carbons  :  Positive,  18mm  cored  ;  Negative,  15mm.  solid.    Current  20  amperes. 
P.O.  between  Carbons,  68  volts.    Length  of  Arc,  18mm . 


THE  APPEARANCE  OF  THE  ARC.  7 

In  Figs.  4  and  5  the  two  arcs  are  of  the  same  length, 
7mm.,  the  current  20  amperes;  but  for  Fig.  4  the  positive 
carbon  was  solid,  and  for  Fig.  5  it  was  cored.  Here,  again,  both 
the  central  purple  part  and  the  green  portion  surround  the 
negative  carbon  to  a  greater  distance  when  the  positive  carbon  is 
solid  than  when  it  is  cored  ;  again,  also,  both  the  central  portion 
and  the  whole  visible  arc  are  larger  with  the  solid  than  with 
the  cored  positive  carbon.  But  in  these  two  figures  the  form  of 
the  central  part  is  also  different.  With  the  cored  carbon  it  is 
gourd-shaped,  with  the  solid,  pear-shaped.  With  the  cored 
carbon  the  arc  has  a  dark  shadow  dividing  it  into  two  unequal 
parts,  with  the  solid  carbon  this  shadow  is  entirely  absent. 
The  tip  of  the  positive  carbon  has  a  longer,  and  the  tip  of  the 
negative  a  shorter  point  with  the  cored  than  with  the  solid 
carbon,  which  may  be  due  to  a  lower  temperature  of  the  crater 
in  the  cored  carbon,  for,  as  will  be  shown  later  (page  14), 
greater  heat  is  indicated  by  a  more  pointed  negative  and  a  less 
pointed  positive  carbon. 

The  balls  on  the  positive  carbon  in  Fig.  4  were  not  really 
luminous  the  whole  time  I  was  drawing  that  figure,  but  every 
now  and  then  there  was  a  little  hiss  caused  by  some  imper- 
fection in  the  carbon,  which  lighted  them  up,  and  during  one 
of  those  periods  I  drew  them. 

In  Fig.  6  the  positive  carbon  was  cored,  and  the  arc  was 
18mm.  in  length,  the  current  still  20  amperes.  In  this  arc 
the  gourd  shape  is  much  accentuated — the  central  part  looks 
almost  like  two  air  balls,  the  one  next  the  positive  carbon 
placed  horizontally,  the  other  placed  vertically  below  it,  and 
touching  the  negative  carbon.  The  vertical  ball  has  inside  it  a 
small  ball  touching  the  negative.  All  three  balls  were  of 
different  shades  of  purple,  the  large  one  near  the  negative 
carbon  was  palest,  the  small  one  was  darker,  and  the  one  near 
the  positive  was  darkest  of  all. 

The  shade  of  the  purple  part  of  the  arc  was  quite  different 
according  as  solid  or  cored  positive  carbons  were  used,  being 
much  bluer  with  solid  than  with  cored  carbons. 

I  tried  to  obtain  an  arc  of  18mm.  with  both  carbons  solid, 
in  order  to  compare  the  two  diagrams,  but  found  it  impossible 
to  maintain  an  arc  of  more  than  14mm.  with  two  18mm.  and 
15mm.  solid  carbons.  Every  time  the  length  of  the  arc  was 


8  THE  ELECTRIC  ARC. 

increased  beyond  this  the  arc  went  out,  because,  as  will  be 
shown  later,  the  E.M.F.  of  the  dynamo  was  insufficient  to 
maintain  a  longer  arc  with  a  current  of  20  amperes  flowing 
when  both  carbons  were  uncored.  The  shape  of  the  14mm. 
arc  showed  no  tendency  towards  the  double  ball  form  observable 
with  the  cored  carbon;  it  retained  the  pear  shape  noticed  in 
Fig.  4.  I  have,  however,  found  a  tendency  to  assume  the 
double  ball  form  with  arcs  maintained  between  solid  carbons 
when  the  current  was  very  small ;  but,  if  the  length  of  the  arc 
is  the  same  in  both  cases,  the  current  has  to  be  much  smaller 
to  produce  this  form  when  the  positive  carbon  is  solid  than 
when  it  is  cored. 

Thus  it  is  clear  that  when  the  current  is  kept  constant, 
altering  the  length  of  the  arc,  alters  both  its  size  and  shape  ; 
and  the  use  of  a  cored  positive  carbon,  instead  of  a  solid, 
changes  the  size,  the  colour,  and,  in  long  arcs,  the  form  of  the 
visible  part  of  the  arc. 

The  diagrams  in  Figs.  7  to  12  are  reproductions  of  some  of  those 
made  by  Prof.  Ayrton's  students.  They  show  very  accurately 
the  shapes  of  the  ends  of  the  carbons  under  the  given  conditions, 
but,  as  in  Fig.  1,  the  dotted  outlines  of  the  arc  must  be  taken  to 
be  only  approximately  correct.  They  show,  for  instance,  that, 
with  a  given  length  of  arc,  the  diameter  of  the  visible  part  of 
the  arc  is  smaller,  the  smaller  the  current,  but  not  with 
absolute  accuracy  exactly  how  much  smaller. 

These  diagrams  have  been  reduced  from  ten  times  the  full 
size  of  the  carbons  to  two-thirds  full  size,  and  arranged  in  order 
of  the  sizes  of  the  carbons,  the  lengths  of  the  arc,  and  the 
currents.  Figures  in  the  same  horizontal  row  are  for  the  same 
length  of  arc  with  different  currents,  and  figures  in  the  same 
vertical  column  are  for  the  same  current  with  different  lengths 
of  arc. 

We  will  first  examine  what  is  the  effect  on  the  shape 
of  the  negative  carbon  of  changing  (1)  the  current  strength, 
and  (2)  the  length  of  the  arc  ;  and  then  we  will  see  what  effect 
these  same  changes  have  on  the  shape  of  the  positive  carbon. 
In  all  the  figures  with  a  short  arc,  say  0'5mm.  (Fig.  7),  the 
negative  carbon  is  quite  pointed,  even  with  a  small  current, 
and  it  becomes  more  and  more  pointed  as  the  current  becomes 
larger  and  larger.  With  a  1  mm.  arc  the  negative  is  less  pointed, 


0  Amperes, 


5  Amperes 


Amperes  130  Ampere" 


p*n 


n 


w 
A 


FIG.  7.  -Carbons,  Positive  (upper)  18mm.  cored.    Negative  (lower)  15mm.  soHd. 


10 


THE  ELECTEIC  ARC. 


both  with  small  and  large  currents,  than  with  a  O'Smm.  arc,  and 
as  the  arc  gets  longer  the  negative  becomes  blunter  and  blunter 
although  in  every  case  it  is  more  pointed  with  a  large  current 
than  with  a  small  one  for  the  same  length  of  arc.  At  last, 
when  the  arc  is  6mm.  long,  the  negative  is  quite  blunt,  even 


2  Amperes 


6  Amperes. 


10  Amperes. 


16  Amperes. 


21  Amperes. 


28  Amperes 


u 


iU 

E  @ff7=& 


p 


y 


n 


FIG.  8.— Carbons,  Positive  (upper)  13ram.  cored.  Negative  (lower)  llmm  solid. 

when  a  current  as  great  as  20  amperes  is  flowing.      Thus,  the 
tip  of  the  negative  is  more  pointed — 

(1)  The  shorter  the  arc, 

(2)  The  larger  the  current. 

In  order  to  understand  the  causes  of  these  phenomena,  we 
must  examine  the  shapes  of  the  negative  tips  a  little  more  closely. 


THE  APPEARANCE  OF  THE  ARC.  11 

Comparing  the  6-ampere  0'5mm.  arc  with  the  6-ampere 
3mm.  arc  in  Fig.  7,  one  sees  that  the  former  is  like  the  latter, 
with  a  sort  of  extra  point  added;  comparing  the  30-ampere 
arcs  for  the  same  two  lengths,  the  same  thing  is  observable, 
only  it  is  much  more  pronounced.  This  sort  of  extra  point 
is,  in  fact,  found  on  all  the  negative  carbons  when  the  arc 
is  short,  whatever  the  current,  and  it  is  not  found  on  any 
when  the  arc  is  long.  This  point  must,  therefore,  depend 
upon  the  carbons  being  near  together,  and  is  caused,  I  think, 
solely  by  carbon  deposited  on  the  negative  tip  from  the 
crater  of  the  positive  carbon.  As  the  arc  is  lengthened,  less 
and  less  of  the  carbon  shot  out  by  the  positive  reaches  the 
tip  of  the  negative  carbon,  and  this  little  extra  tip  becomes 
smaller  and  smaller,  and  finally  disappears. 

When  the  distance  between  the  carbons  is  great  and  the 
current  small,  the  arc  often  plays  about  the  edges  of  the 
carbons,  sometimes  seeming  to  travel  round  and  round  them, 
sometimes  remaining  stationary  in  one  place  for  a  short  time, 
and  then  going  to  another,  and  so  on,  but  always  trying  to 
make  itself  as  long  as  possible.  But  in  some  cases,  however 
the  positive  end  of  the  arc  may  move,  the  negative  end  appears 
to  remain  in  the  same  place,  so  that  the  negative  bright  spot 
remains  fixed  in  position,  and  when  this  is  so,  on  extinguishing 
the  arc,  it  is  found  that  there  is  a  small  crater  at  the  end  of 
the  negative  carbon. 

It  is  possible  that  this  crater  would  always  exist  in  the 
negative  carbon  were  it  not  that  when  the  arc  is  shorter  the 
crater  is  constantly  filled  up  by  the  carbon  deposited  on  it  from 
the  positive  carbon. 

When  the  arc  is  very  short,  and  the  current  large  enough  to 
cause  hissing,  the  deposition  takes  place  so  rapidly  as  to  cause 
a  "  mushroom  "  to  form,  such  as  may  be  seen  in  the  25-ampere 
1mm.  arc  in  Fig.  9.  When  the  arc  is  short,  even  when  it  is  silent, 
the  deposition  is  still  often  rapid  enough  to  cause  the  negative 
carbon  to  grow  longer  instead  of  shorter,  and  this  fact  alone 
would  seem  to  prove  that  the  extra  tip  noticed  on  the  negative 
carbon  with  short  arcs  is  caused  by  carbon  deposited  on  it  from 
the  crater. 

It  is  true  that  with  large  currents  the  tip  of  the  negative 
carbon  is  somewhat  pointed,  even  when  the  arc  is  not  very 


12 


THE  ELECT EIC  ARC. 


3  Amperes.      6  Amperes.  12  Amperes    16  Amperes.  26  Amperes.     30  Amperes 


ST1 


A 


u 


IS 


u 


FIG.  9.— Carbons,  Positive  (upper)  9mm.  cored.     Negative  (lower)  8mm.  solid- 


THE  APPEARANCE  OF  THE  ARC.  13 


short,  as  in  the  30-ampere  3mm.  arc  in  Fig.  H,  but  it  seems 
to  be  pointed  in  a  different  way.  The  end  of  the  carbon  has 
no  little  extra  tip  on  it,  but  becomes  more  nearly  cone  shaped, 
and  this  sort  of  pointing  is  attributable,  I  think,  to  quite  a 
different  cause — namely,  the  burning  away  of  the  carbon.  Most 
of  the  heating  of  the  negative  carbon  takes  place  from  the  out- 
side, and  is  caused  partly  by  radiation  from  the  crater  and 
partly  by  the  volatile  carbon  giving  up  its  heat  to  it.  When 
the  current  is  small  the  heat  is  comparatively  small ;  there- 
fore only  a  thin  layer  and  a  short  length  of  the  negative  carbon 
is  made  hot  enough  to  burn  away,  and  consequently  the 
point,  which  is  the  result  of  the  burning  away,  is  short  and 
blunt. 

With  large  currents,  however,  the  heat,  being  greater, 
reaches  farther,  both  through  and  down  the  negative  carbon, 
and  the  resulting  tip  is  longer  and  more  slender.  It  is  more 
or  less  conical,  because  the  parts  farther  away  from  the  positive 
carbon  get  less  heat,  and,  therefore,  a  thinner  layer  of  them  is 
burnt  away. 

Thus  with  short  arcs  there  are  two  distinct  causes  tending 
to  give  the  tip  of  the  negative  carbon  its  special  shape,  whereas 
with  long  arcs  one  of  these  causes  is  nearly  or  quite  inoperative, 
hence  the  difference  of  character  of  the  shapes  of  the  negative 
carbons  in  the  two  cases. 

It  is  much  more  difficult  to  find  out  what  happens  to  the  posi- 
tive carbon  than  to  the  negative  when  the  arc  is  lengthened  or  the 
current  increased,  because  that  carbon  is  very  rarely  luminous 
over  the  whole  length  of  its  tapering  part.  As  has  already  been 
pointed  out  (page  4),  the  negative  carbon  is  always  bathed  in 
the  light  from  the  positive,  and,  therefore,  its  shape  is  very  easily 
discerned;  but  the  positive  sends  all  its  own  light  away  from  it, 
and  can  receive  little,  if  any,  from  the  negative.  But  even  so, 
by  comparing  the  carbons  in  those  cases  in  which  it  has  been 
possible  to  trace  the  positive  carbon  to  its  unburnt  part,  it 
may  be  perceived  that  it  also  tapers  more  with  a  short  arc  than 
with  a  long  one  when  the  same  current  is  flowing,  and  has 
a  longer,  but  less  pointed,  tapering  part  with  a  large  current 
than  with  a  small  one. 

For  instance,  take  the  6-arnpere  0'5mm.  arc  and  the 
G-ampere  5rnm.  arc  in  Fig.  7,  evidently  the  positive  carbon 


14  THE  ELECTEIC  ARC. 

tapers  more  in  the  former  than  in  the  latter,  and  in  the  5mm. 
arcs  in  the  same  figure  the  positive  carbon  has  a  longer  tapering 
part  with  25  amperes  than  with  IT  amperes.  Also  it  will  be 
found  that  wherever  the  craters  show,  the  diameter  of  the  crater 
is  greater  with  a  larger  current  than  with  a  smaller  one  for  the 
same  length  of  arc  and  greater  with  a  longer  arc  than  with 
a  shorter  one  when  the  same  current  is  flowing. 

Apparently  what  happens  is  this.  The  positive  carbon  is 
consumed  in  two  ways — (1)  by  being  shot  out  from  the  crater 
either  in  the  form  of  vapour  or  of  small  particles,  (2)  by  burn- 
ing in  combination  with  air.  It  is  not  probable  that  volatilisa 
tion,  which  requires  an  enormous  temperature,  can  take  place, 
if  it  takes  place  at  all,  anywhere  except  at  the  surface  of  the 
crater,  and  perhaps  at  the  parts  of  the  tip  immediately  surround- 
ing that  surface ;  therefore  all  the  shaping  of  the  positive 
carbon,  except  the  formation  of  the  crater,  must  depend  upon 
its  burning  in  combination  with  air.  At  the  extreme  tip  the 
burning  will  take  place  most  rapidly,  because,  owing  to  the 
immediate  vicinity  of  the  crater,  the  surface  carbon  will  be 
hotter  there  than  anywhere  else,  and  the  larger  the  crater  the 
more  rapidly  the  tip  will  burn  away.  Thus,  instead  of 
becoming  more  pointed  as  the  current  increases,  the  positive 
carbon  actually  becomes  less  pointed,  because  the  tip  is  con- 
sumed so  much  faster  than  the  sides.  Although  it  is  less 
slender,  the  point  is  longer,  however,  because  the  increased 
amount  of  volatile  carbon  extends  farther  up  the  sides,  and 
thus  burns  away  a  longer  portion  of  the  carbon. 

When  the  arc  is  short,  the  volatile  carbon,  not  finding  room 
between  the  tips,  spreads  out  farther,  and  so  also  spreads  farther 
along  the  surfaces  of  the  carbons  and  causes  them  to  burn 
away  to  a  greater  distance  than  when  the  arc  is  long.  In  fact, 
a  given  amount  of  volatile  carbon  must  take  up  a  given  space 
with  a  given  pressure  all  round  it.  If  it  can  get  this  space  be 
tween  the  carbons,  it  takes  it ;  if  not,  it  extends  itself  sideways 
and  longways,  and  hence  the  ends  of  both  the  carbons  have 
longer  points  with  short  arcs  than  with  long  ones,  when  the 
current  is  the  same  for  each  length  of  arc. 

Fig.  10  shows  very  well  the  alteration  that  takes  place  in 
the  shapes  of  the  carbons  when  the  current  is  suddenly 
changed  from  a  higher  to  a  lower,  and  from  a  lower  to  a 


THE  APPEARANCE  OF  THE  ARC.  1& 

higher  value.  The  left-hand  figure  shows  particularly  well  the 
alteration  in  the  negative  carbon.  In  this  case,  after  the 
carbons  had  been  formed  by  a  current  of  30  amperes,  the  current 
was  suddenly  changed  to  one  of  4  amperes,  and  three  minutes 
afterwards  the  dotted  line  diagram  was  taken,  showing  th& 
negative  carbon  with  a  long  tapering  end.  But  with  the 
smaller  current  the  volatile  carbon  did  not  extend  down  nearly 
as  far  as  before;  consequently,  as  the  tip  of  the  carbon  was 
gradually  burnt  away,  the  tapering  of  new  parts  of  thi& 


FIG.  10. — Carbons:  Positive  (upper)  13mm.  cored.  Negative  (lower) 
llmm.  solid.  Length  of  Arc  4mm.  A,  Current  suddenly  changed  from' 
30  amperes  to  4  amperes.  Dotted  lines  show  the  shapes  of  the  Carbons. 
3  minutes  after  the  change.  Continuous  lines  show  their  shapes  25  minutes 
after.  B,  Current  suddenly  changed  from  10  amperes  to  30  amperes. 

negative  carbon  was  not  kept  up.  Hence,  in  25  minutes  after 
the  current  had  been  reduced  from  30  to  4  amperes,  the 
end  of  the  negative  carbon  had  become  blunt,  as  shown  by  the 
continuous  outside  line.  The  small  piece  at  the  top  of  th& 


105  Amp. 


3     Amp    14  Amp. 


FIG.  11. — A,  Carbons :  Positive  (upper)  13mm.  solid.  Negative  (lower) 
llmm.  solid.  Length  of  Arc,  Omm.  B  and  C,  Carbons  :  Positive  (upper) 
9mm.  solid.  Negative  (lower)  8mm.  solid.  Length  of  Arc,  4mm. 

negative  carbon,  which  is  of  much  smaller  diameter  than  the 
remainder,  indicates  how  far  down  the  burning  action  of 
the  amount  of  volatile  carbon  given  off  by  the  smaller  current 
extended. 

Fig.  1 1  shows  the  arc  with  solid  carbons.  In  B  a  current 
of  3  amperes  was  flowing  through  an  arc  of  4mm.  Com- 


16 


THE  ELECTRIC  AEG. 


paring  this  with  the  arc  of  the  same  length,  and  with  the 
same  current  in  Fig.  9,  for  which  the  carbons  were  of  the  same 
size,  the  only  thing  to  notice  is  that,  as  in  Figs.  4  and  5,  the 
visible  arc,  as  shown  by  the  dotted  lines,  is  larger  with  a  solid 
than  with  a  cored  positive  carbon.  Experience  has  shown  that 
this  is  quite  correct.  In  every  case  in  which  I  have  been  able 
to  compare  the  sizes  of  the  arcs  obtained  with  solid  and  cored 
positive  carbons  under  similar  conditions,  I  have  found  the 
area  of  the  visible  part  to  be  larger  when  the  carbons  were 
both  solid. 


V 

A 

4  Amperes. 


6  Amperes. 


10  Amperes. 


- 


16  Amneres 


A 


24  Amperes.j 


FIG.  12. — Carbons  :  Positive  (upper)  13mm.  solid.     Negative  (lower)  llmm. 
cored.     Length  of  Arc,  4mm. 

In  Fig.  12  the  positive  carbons  were  solid  and  the  negatives 
cored,  with  the  result  that  the  latter  were  burnt  away  farther 
down  than  they  would  have  been  if  the  cases  had  been 
reversed,  and  the  negative  carbons  had  craters  in  them. 

SUMMARY. 

When  a  direct-current  silent  arc  is  maintained  between 
vertical  carbon  rods,  the  positive  carbon  being  uppermost — 

I.  The  tip  of  the  positive  carbon  is  white  hot,  and  the  tip 
of  the  negative  has  a  white-hot  spot  on  it. 

II.  A  white-hot  crater  forms  in  the  end  of  the  positive  carbon, 
and  a  more  or  less  blunt  point  forms  on  the  end  of  the  negative. 

III.  The  space  between  the  two  is  filled  by  a  violet  light, 
the  shape  of  which  is  defined  by  a  shadow,  which  in  its  turn  is 
bounded  at  its  sides  by  a  green  light. 

IV.  The  ends  of  both  carbons  are  tapered,  and  the  lengths 
of  the  tapering  parts  are  increased   both  by  increasing   the 
current  and  by  shortening  the  arc. 

V.  The   diameter   of   the  crater   increases   as    the    current 
increases,  and  also  as  the  length  of  the  arc  increases. 


THE  APPEARANCE  OF  THE  ARC.  17 

VI.  With  uncored  carbons  the  violet  part  of  the  arc  is  bluer, 
and  all  parts  of  the  arc  are  larger  than  with  cored  carbons. 

VII.  With  uncored  carbons  the  violet  part  of  the  arc  is  of 
the  form  of  an  oblate  spheroid  when  the  arc  is  short,  pear- 
shaped  when  it  is  long,  and  gourd-shaped  when  it  is  long  and 
the  current  is  very  small. 

VIII.  With  cored  carbons  the  violet  part  is  of  the  form  of  an 
oblate  spheroid  when  the  arc  is  short,  gourd-shaped  when  it 
is  long,  and  sometimes  almost  of  the  shape  of  a  figure  of  8 
when  the  arc  is  very  long  for  the  current  flowing. 

IX.  When  the  negative  carbon  is  cored,  a  crater  is  formed  in 
its  tip  exactly  as  if  it  were  a  positive  carbon. 


CHAPTER  II. 


A  SHORT  HISTORY  OF  THE  ARC. 

ON  March  20,  1800,  Volta  wrote  his  first  letter  announcing  the 
discovery  of  his  pile.  The  news  was  received  by  the  scientific 
world  with  an  enthusiasm  only  to  be  paralleled  by  that  which 
was  aroused  at  the  end  of  1895  by  the  discovery  of  the  X-rays 
by  Rontgen.  New  possibilities  were  opened  up,  and  none  could 
tell  whither  they  might  lead.  A  sort  of  experimental  fever 
seized  upon  mankind,  or  at  least  upon  the  scientific  part  of  it, 
and  Paper  after  Paper  was  written  describing  new  and  inte- 
resting results  obtained  with  the  pile.  So  numerous  were 
these  Papers  in  the  course  of  the  next  year  that  in  the  middle 
of  1801  a  certain  Dr.  Benzenberg  wrote  to  the  editor  of  Gil- 
bert's Annalen :  "  Could  not  the  Annalen,  in  consideration  of 
its  object,  be  a  little  more  varied?  Galvanism,  interesting  as 
it  is,  is  still  only  a  very  small  part  of  physics.  We  can  appa- 
rently only  expect  any  real  advance  in  knowledge  from  such 
work  as  is  carried  oat  on  a  large  scale,  and  not  from  each 
experimenter,  whose  slight  knowledge  and  small  apparatus 
allow  him  to  discover  only  what  ten  others  have  already  found 
out  before  him." 

The  first  question  to  which  an  answer  was  sought  by  all 
these  numerous  observers  was,  What  is  the  nature  of  the  new 
current1?  Is  it  a  "galvanic"  current?  is  it  "common  elec- 
tricity "  ?  or  is  it  neither  ?  Odd  as  it  may  now  seem,  many 
Papers  were  written  to  prove  that  the  voltaic  current  had 
nothing  in  common  with  either  galvanism  or  common — i.e., 
f  fictional — electricity. 

The  early  experiments  may  be  divided  into  three  classes, 
viz. : — (1)  Those  which  dealt  with  the  effect  of  the  current  on 
living  things.  (2)  Those  which  produced  chemical  decompo- 

c2 


20  THE  ELECTRIC  ABC. 

sition  of  inorganic  matter,  particularly  of  water.  (3)  Those 
which  dealt  with  the  heating  power  of  the  current,  more  par 
ticularly  with  the  sparks  produced  by  making  or  breaking  a 
circuit.  These  last  experiments  led  directly  to  the  discovery 
of  the  arc,  and  are,  therefore,  the  only  ones  with  which  we  ar& 
immediately  concerned. 

One  of  the  most  ordinary  ways  of  using  frictional  electricity 
was  to  produce  sparks,  and  therefore  one  of  the  most  obvious- 
methods  of  showing  that  the  voltaic  current  was  of  the  same 
nature  as  "common  electricity"  was  to  make  a  spark  by  bringing 
together  two  conductors  attached  to  the  terminals  of  a  battery. 
Most  of  the  early  observers  were  able  to  do  this ;  but  Sir 
Humphry  Davy,  towards  the  end  of  October,  1800,  was  the 
first  to  try  tha  effect  of  using  as  conductors  two  pieces  of 
well-burned  charcoal,  a  substance  which  Priestley  had  already 
shown  to  be  a  good  conductor  of  electricity.*  In  speaking  of 
the  result  of  using  charcoal  Davy  said  : — 

"  I  have  found  that  this  substance  possesses  the  same  pro- 
perties as  metallic  bodies  in  producing  the  shock  and  spark 
when  made  a  medium  of  communication  between  the  ends  of 
the  galvanic  pile  of  Signer  Volta." l 

Later,  in  a  lecture  before  the  Royal  Institution,  given  in 
1801,  Sir  Humphry  mentioned  that  the  spark  passing  between 
two  pieces  of  well-burned  charcoal  was  larger  than  that  passing 
between  brass  knobs,  "  and  of  a  vivid  whiteness ;  an  evident 
combustion  was  produced,  the  charcoal  remained  red  hot 
for  some  time  after  the  contact,  and  threw  off  bright 
coruscations."8 

This  is  evidently  the  description,  not  of  an  arc,  but  of  a 
spark.  For  the  essence  of  an  arc  is  that  it  should  be  continuous, 
and  that  the  poles  should  not  be  in  contact  after  it  has  once 
started.  The  spark  produced  by  Sir  Humphry  Davy  was 
plainly  not  continuous ;  and  although  the  carbons  remained  red 
hot  for  some  time  after  contact,  there  can  have  been  no  arc 
joining  them,  or  so  close  an  observer  would  have  mentioned  it. 

*  Priestley's  "  History  of  Electricity,"  p.  598. 

1  To  avoid  the  continual  use  of  footnotes,  the  titles  of  the  Communica- 
tions referred  to  in  the  text,  and  of  others  of  interest  on  the  subject,  are 
arranged  in  chronological  order  at  the  end  of  the  Chapter.  The  numbers 
in  the  text  refer  to  the  numbers  in  this  list. 


A  SHORT  HISTORY  OF  TEE  ARC.  21 

la  another  lecture,  delivered  at  the  Royal  Institution  in  1802, 
in  which  he  spoke  of  trying  the  effect  of  the  electrical  ignition 
of  dry  charcoal  upon  muriatic  acid  gas  confined  over  mercury, 
Davy  said,  "The  charcoal  was  made  white  hot  by  successive 
contacts  made  for  nearly  two  hours."  9 

Hence  it  is  quite  certain,  not  only  that  he  knew  nothing  about 
the  arc  at  that  time,  but  that  the  battery  he  used  was  incap- 
able of  maintaining  an  arc,  otherwise  the  successive  contacts 
would  have  been  unnecessary. 

In  reading  the  accounts  of  the  first  experiments  made  upon 
the  sparks  produced  by  batteries,  it  seems  as  if  the  arc  could 
hardly  fail  to  be  discovered  very  soon ;  as  if  in  each  case  the 
next  experiment  must  be  the  one  that  will  produce  a  veritable 
arc.  But  this  leaves  out  of  account  the  resistance  of  the 
batteries  used.  The  first  batteries  were  mostly  made  of  coins, 
such  as  the  half-crown  in  England,  and  the  double  louis  d'or 
in  France  and  Italy,  divided  from  pieces  of  zinc  of  the  same 
size  and  shape  by  discs  of  cardboard  soaked  in  dilute  acid. 
The  resistance  of  such  a  battery  would  be  very  great  compared 
with  what  it  should  be  in  order  to  maintain  an  arc,  and  the 
pissing  of  a  spark  would  so  lower  the  P.D.  between  the 
terminals  that  no  other  spark  could  pass  till  the  battery  had 
somewhat  recovered.  In  fact,  these  batteries,  having  a  high 
E.M.F.  and  great  resistance,  especially  when  they  consisted  of 
many  pairs  of  plates,  were  exactly  adapted  to  imitate  the  action 
of  a  frictional  machine,  and  therefore  to  show  that  the  voltaic 
current  was  an  electric  current — which  was  all  that  their 
devisers  attempted  at  first  to  prove. 

Cruickshanks  very  early  discarded  the  cardboard  discs,  and 
arranged  his  pairs  of  plates  in  troughs  containing  dilute  acid ; 
and  English  experimenters  immediately  recognised  the  advan- 
tage of  this  arrangement.  Most  foreigners,  however,  continued 
for  a  long  time  to  use  the  more  primitive  form  of  battery,  and 
hence,  although  they  made  very  numerous  experiments  upon 
the  sparks  produced  by  batteries  both  with  charcoal  and  with 
metal  terminals,  their  sparks  probably  remained  sparks,  and 
did  not  develop  into  arcs. 

The  diminution  in  the  resistance  of  the  battery  caused 
-by  the  use  of  larger  plates  was  discovered  early  in  1801  by 
Fourcroy,  Vauquelin  and  Thenard,  who  tried  the  effect  of 


22  THE  ELECTRIC  ARC. 

plates  of  different  sizes.  With  eight  pairs  of  plates  eight 
inches  in  diameter  they  found  that  they  could  produce  sparks 
brighter  than  with  120  pairs  of  smaller  plates.  Pfaff  of  Kiel 
says,  in  describing  these  experiments,  "  The  rays  streamed  on 
all  sides  several  lines  wide,  thej  crackling  was  very  sharp,  and 
in  oxygen  the  wire  burnt  with  a  vivid  flame." 5  Hence,  the 
experimenters  deduced  the  fact  that  batteries  with  large 
plates  were  the  best  to  use  for  producing  sparks  and  observing 
the  heating  effect  of  the  current. 

For  some  time  after  1801  Davy  and  the  other  English 
observers  confined  themselves  principally  to  experimenting  upon 
the  chemical  effects  of  the  current  in  decomposing  substances 
which  had  proved  refractory  until  this  powerful  agent  was 
discovered.  On  the  Continent,  however,  it  was  otherwise ;  the 
spark  had  its  full  share  of  attention  for  its  own  sake.  In 
France  Fourcroy,  Yauquelin  and  Thenard,  and  in  Germany 
and  Austria  Hitter,  Tromsdorff,  Gilbert  and  Pfaff,  all  experi- 
mented with  it,  and  melted  and  burnt  gold  and  silver  leaf  and 
thin  wires  by  means  of  it,  causing  flames  to  arise  between 
the  two  poles.  Hence  it  is  impossible  to  say  when  and  by 
whom  the  arc  was  really  discovered.  For  the  arc,  after  all,  is 
but  a  spark,  which  continues  after  the  poles  are  separated,  and 
which  melts  and  burns  or  volatilises  the  substance  of  the  poles. 
These  experimenters  probably  did  not  see  any  great  distinction 
between  a  continuous  and  rapidly  following  shower  of  sparks 
and  a  single  spark  which  continued.  They  never  mentioned  the 
time  of  duration  of  their  sparks,  and  they  were  so  much 
accustomed  to  sparks  passing  between  the  two  poles  of  a 
frictional  machine  without  actual  contact  taking  place,  that  it 
is  very  possible  that  a  spark  continuing  to  exist  after  the  poles 
had  been  separated  would  appear  quite  natural  to  them. 

The  following  abstracts  and  extracts  will  suffice  to  show  the 
impossibility  of  judging  when  and  by  whom  the  arc  was 
really  discovered. 

In  1801  Fourcroy,  Vauquelin  and  Thenard,  with  a  battery 
of  plates  a  foot  square,  "  ignited  wires  immediately,  and  in 
oxygen  they  burnt  with  a  very  vivid  light."  10 

In  the  same  year  Hitter,  of  Jena,  wrote  to  Gilbert,  the 
Editor  of  the  Annalen,  that  in  trying  to  observe  which  end  of 
a  zinc-silver  battery  evolved  the  greater  heat,  he  found  that, 


A  SHORT  HISTORY  OF  THE  ARC.  23 

when  a  silver  leaf  was  attached  to  the  zinc  end  and  well  burnt 
clean  charcoal  to  the  silver  end,  the  silver  could  be  completely 
burnt  away  by  making  contact  between  it  and  the  charcoal ; 
while,  if  the  position  of  the  silver  and  charcoal  were  reversed, 
the  silver  did  not  burn,  but  there  appeared  on  the  charcoal 
"yellow,  more  than  instantaneous  sparks,  which  were  not  seen 
in  the  other  experiment,  quite  sharp  edges  of  the  charcoal 
appeared  to  become  blunt,  in  short,  everything  pointed  to  a 
combustion  of  the  charcoal."6  (The  italics  are  Hitter's.) 

In  the  same  letter  Ritter  mentioned  that  when  he  had  iron 
wires  on  each  side  of  the  battery,  and  a  spark  passed,  they  some- 
times became  melted  together,  and  he  had  to  use  some  force  to 
separate  them.  He  also  said,  "  I  have  spoken  above  of  the  big 
spark  that  the  battery  of  224  plates  gave  at  the  closing  of  the 
silver  wire  with  the  zinc  plate  above  it.  But  also  on  breaking 
the  circuit  it  gave  sparks.  ...  On  quickly  drawing  away 
the  iron  wire  attached  to  the  silver  plate  in  a  vertical  direction 
from  the  surface  of  the  zinc  plate,  a  small  red  spark  appeared, 
which  seemed  to  come  with  more  certainty  when  the  circuit 
had  been  closed  for  some  time  before  it  was  opened." 

In  1802  was  published  the  following  account  of  experiments 
made  in  April  of  the  same  year  by  Prof.  Tromsdorff,  at 
Erfurth.  A  leaf  of  fine  gold,  after  having  been  fixed  to  the 
zinc  end  of  the  pile,  ignited  and  burnt  with  a  crackling  noise 
when  the  wire  of  the  copper  side  was  brought  in  contact  with 
it.  "  Other  metals  burnt  with  flames  of  different  colours. 
.  .  .  .  To  prove  that  the  ascension  of  the  metals  is  a  true 
oxidation,  the  experiments  may  be  performed  in  a  hollow  glass 
sphere ;  the  oxide  will  adhere  to  the  sides  of  the  glass,  and 
may  be  collected."  n 

The  next  account,  also  in  1802,  is  anonymous:  "Two 
carbon  rods,  which  were  attached  as  conductors  to  a  battery  of 
26  pairs,  were  brought  into  contact  in  a  receptacle  full  of 
oxygen.  They  caught  fire  and  burnt."  12 

In  1803  Mr.  Pepys,  an  Englishman,  with  a  battery  of  60 
pairs  of  zinc  and  copper  plates,  disposed  in  two  troughs,  after 
the  plan  suggested  by  Cruickshanks,  found  that  "  carbons  of 
boxwood  not  only  ignited  at  their  point  of  contact,  but  glowed 
red  for  a  distance  of  quite  two  inches,  and  continued  to  do  so 
for  some  time."  13 


24  THE  ELECTRIC  ARC. 

In  1804  Cuthbertson,  another  Englishman,  wrote  "charcoal 
was  deflagrated  and  ignited  for  about  one  inch  by  a  battery."  u 

From  1804  till  1807  very  little  that  was  fresh  was  done. 
The  old  experiments  were  repeated  by  many  observers,  but  no 
advance  was  made.  In  1807  Cuthbertson  wrote  more  fully  on 
the  subject  in  his  book  on  "  Practical  Electricity  and  Galvan- 
ism," quoted  by  Prof.  Silvanus  Thompson  in  his  Cantor  Lectures 
of  1895  :— 

"  Experiment  209,  Deflagration  of  Charcoal  by  Galvanic 
Action. — -The  charcoal  for  this  experiment  must  be  made  of 
some  very  close  grained  wood,  such  as  boxwood  or  lignum  vitse, 
well  charred,  cut  into  pieces  about  an  inch  long,  one  end  being 
scraped  to  a  point,  and  the  other  so  that  it  can  be  held  by  a 
port-crayon  fixed  to  the  end  of  one  of  the  directors ;  then, 
approaching  the  point  of  charcoal  to  the  end  of  the  other 
director,  light  will  either  appear  or  the  charcoal  will  be  set  on 
fire.  The  particular  management  required  should  be  obtained 
by  trials.  The  light,  when  properly  managed,  exceeds  any  other 
artificial  light  ever  yet  produced."15 

In  his  Bakerian  Lecture  delivered  on  November  16tb,  1809, 
Davy  said  that  when  a  current  was  sent  by  1,000  double  plates 
each  four  inches  square  through  potassium  vapour  between 
platinum  electrodes,  over  nitrogen  gas,  a  vivid  white  flame 
arose.  "  It  was  a  most  brilliant  flame,  of  from  half  an  inch  to 
one  and  a  quarter  inches  in  length."  ir 

In  the  library  of  the  Royal  Institution  are  two  large  thick 
volumes  of  manuscript  notes,  bound  in  leather,  and  carefully 
paged.  These  are  Sir  Humphry  Davy's  laboratory  notes  for 
the  years  1805  to  1812.  Faraday,  who  paged  them,  wrote  a 
short  note  at  the  beginning  of  each  volume,  saying  that  Davy 
had  a  way,  before  he  went  to  live  at  the  Royal  Institution, 
of  tearing  out  pages  from  his  note  books,  and  taking  them 
home  with  him  to  think  over ;  but  that  these  two  volumes  being 
complete,  he,  Faraday,  had  paged  them.  Finding  that  there 
was  no  more  direct  mention  of  the  arc  than  the  above  in  any  of 
Sir  Humphry  Davy's  published  works,  nor  in  the  Philosophical 
Transactions  of  the  Royal  Society,  nor  in  the  Philosophical 
Magazine  before  1812,  I  searched  through  these  two  volumes 
for  any  record  of  the  first  discovery  of  the  arc,  and  found  the 
following  two  passages  which  I  am  kindly  permitted  to  publish. 


A  SHORT  HISTORY  OF  THE  ARC.  25 

"  April  20,  1808. 

"  A  given  quantity  of  muriatic  acid  gas  was  acted  upon  by 
dry  charcoal ;  there  was  a  continued  vivid  light  in  the  galvanic 
circuit." 

"August  23,  1809. 

"  AN  EXPERIMENT  TO  ASCERTAIN  WHETHER  ANY  HEAT  SENSIBLE 
TO  THE  THERMOMETER  IS  PRODUCED  BY  THE  ELECTRIC  FLAME  IN 
VACUO. 

"The  jar  which  contained  the  apparatus  consisted  of  a 
concave-plated  mirror,  so  situated  as  to  collect  the  light 
radiating  from  the  charcoal,  and  to  concentrate  them  (sic)  on 
the  bulb  of  a  mercurial  thermometer,  which,  together  with  the 
wires  holding  the  two  pieces  of  charcoal,  passed  through  a  collar 
of  leather.  No  heat  was  apparently  produced  by  the  light 
excited  in  vacuo.  The  air  being  introduced,  immediately  the 
column  of  mercury  rose.  The  light  in  vacuo  was  in  part  of 
a  beautiful  blue  colour,  and  attended  with  bright  red  scintil- 
lations."16 

The  "  vivid  light  "  referred  to  in  the  first  of  these  extracts  is 
plainly  an  arc  ;  but  in  the  second,  the  words  "  electric  flame  " 
leave  no  room  for  doubt,  not  only  that  Davy  was  using  an 
arc,  but  that  it  was  no  new  phenomenon  to  him.  When  was  the 
arc  discovered  then,  and  by  whom  ?  Was  it  not  simply  evolved 
through  experiments  on  sparks  and  on  the  burning  of  metals, 
so  gradually  that  no  one  realised  it  as  a  separate  phenomenon 
until,  with  the  large  battery  subscribed  for  by  the  members  of 
the  Royal  Institution,  Davy  made  a  very  long  horizontal  arc 
which  formed  a  true  arch,  and  therefore  appealed  to  the 
imagination  as  something  new  ?  Even  then,  however,  it  was 
chiefly  considered  interesting  as  showing  the  immense  power  of 
the  battery,  as  will  be  seen  from  the  following  accounts,  the  first 
of  which,  taken  from  the  Monthly  Maya.zine,  a  sort  of  popular 
journal  of  art,  science,  and  literature,  is,  I  believe,  the  first 
definite  published  account  of  the  arc.  The  second  is  from 
Davy's  "  Elements  of  Chemical  Philosophy,"  published  in  1812. 

"At  the  concluding  lecture  for  the  season  at  the  Koyal 
Institution  the  large  voltaic  apparatus,  consisting  of  2,000 
double  plates,  four  inches  square,  was  put  in  action  for  the  first 
time.  The  effects  of  this  combination,  the  largest  that  has 
been  constructed,  were  of  a  very  brilliant  kind.  The  spark,  the 


26  THE  ELECTRIC  ARC. 

light  of  which  was  so  intense  as  to  resemble  that  of  the  sun, 
struck  through  some  lines  of  air,  and  produced  a  discharge 
through  heated  air  nearly  three  inches  in  length,  and  of  a  dazzling 
splendour.  Several  bodies  which  had  not  been  fused  before 

were  fused  by  this  flame Charcoal  was  made 

to  evaporate,  and  plumbago  appeared  to  fuse  in  vacuo. 
Charcoal  was  ignited  to  intense  whiteness  by  it  in  oxymuriatic 
acid,  and  volatilised  by  it,  but  without  being  decomposed." 19 

Here  is  Davy's  own  account  : — 

"  The  most  powerful  combination  that  exists  in  which 
number  of  alternations  is  combined  with  extent  of  surface,  is 
that  constructed  by  the  subscriptions  of  a  few  zealous 
cultivators  and  patrons  of  science,  in  the  laboratory  of  the 
Royal  Institution.  It  consists  of  two  hundred  instruments, 
connected  together  in  regular  order,  each  composed  of  ten 
double  plates  arranged  in  cells  of  porcelain,  and  containing 
in  each  plate  thirty-two  square  inches,  so  that  the  whole 
number  of  double  plates  is  2,000,  and  the  whole  sur- 
face 128,000  square  inches.  This  battery,  when  the  cells 
were  filled  with  one  part  of  nitric  acid  and  one  part  of 
sulphuric  acid,  afforded  a  series  of  brilliant  and  impressive 
effects.  When  pieces  of  charcoal,  about  an  inch  long  and  one- 
sixth  of  an  inch  in  diameter,  were  brought  near  each  other 
(within  the  thirtieth  or  fortieth  part  of  an  inch),  a  bright  spark 
was  produced,  and  more  than  half  the  volume  of  the  charcoal 
became  ignited  to  whiteness,  and  by  withdrawing  the  points 
from  each  other  a  constant  discharge  took  place  through  the 
heated  air,  in  a  space  at  least  equal  to  four  inches,  producing  a 
most  brilliant  ascending  arch  of  light,  broad  and  conical  in 
form  in  the  middle. 

"When  any  substance  was  introduced  into  this  arch,  it 
instantly  became  ignited ;  platina  melted  as  readily  in  it  as 
wax  in  the  flame  of  a  common  candle  •  quartz,  the  sapphire, 
magnesia,  lime,  all  entered  into  fusion;  fragments  of  diamond, 
and  points  of  charcoal  and  plumbago,  rapidly  disappeared  and 
seemed  to  evaporate  in  it,  even  when  the  connection  was  made 
in  a  receiver  exhausted  by  the  air  pump ;  but  there  was 
no  evidence  of  their  having  previously  undergone  fusion. 

"  When  the  communication  between  the  points  positively  and 
negatively  electrified  was  made  in  air  rarefied  in  the  receiver  of 


A  SHORT  HISTORY  OF  THE  ARC.  27 

the  air  pump,  the  distance  at  which  the  discharge  took  place 
increased  as  the  exhaustion  was  made,  and  when  the  atmos- 
phere in  the  vessel  supported  only  one-fourth  of  an  inch  of 
mercury  in  the  barometrical  gauge,  the  sparks  passed  through 
a  space  of  nearly  half  an  inch  ;  and,  by  withdrawing  the  points 
from  each  other,  the  discharge  was  made  through  six  or  seven 
inches,  producing  a  most  beautiful  coruscation  of  purple  light, 
the  charcoal  became  intensely  ignited,  and  some  platinum  wire 
attached  to  it  fused  with  brilliant  scintillations,  and  fell  in 
large  globules  upon  the  plate  of  the  pumps.  All  the 
phenomena  of  chemical  decomposition  were  produced  with 
intense  rapidity  by  this  combination.  When  the  points  of 
charcoal  were  brought  near  each  other  in  non-conducting  fluids, 
such  as  oils,  ether,  and  oxymuriatic  compounds,  brilliant  sparks 
occurred,  and  elastic  matter  was  rapidly  generated ;  and  such 
was  the  intensity  of  the  electricity  that  sparks  were  produced 
even  in  good  imperfect  conductors,  such  as  the  nitric  and 
sulphuric  acids."  20 


FIG.  13. — Horizontal  Arc,  copied  from  the  figure  in  "  Davy's  Elements  of 
Chemical  Philosophy." 

This  very  definite  and  beautiful  description  of  the  arc  leaves 
no  doubt  that  Sir  Humphry  Davy  was  the  first  to  show  the  long 
horizontal  arch  of  flame  that  gives  the  arc  its  name;  although  the 
question  whether  or  not  he  was  the  first  person  to  obtain  an  arc 
of  any  shape  and  size  will  probably  remain  for  ever  a  mystery. 

After  1812  no  important  work  on  the  arc  w»-.s  done  till  1820, 
when  Arago  suggested  that  it  would  probably  behave  like  a 
flexible  conductor,  and  both  attract  a  magnet  and  be  attracted 
by  it.  He  thought  a  very  powerful  battery  was  needed  to  pro- 
duce such  an  arc  as  would  show  the  deflection;  and  not  having 
one  himself,  he  suggested  that  someone  who  had  should  try  the 
experiment.21  Meanwhile  Davy,  working  on  the  same  lines, 
had  come  to  the  same  conclusion;  and  without  having  seen 
Arago's  suggestion,  which,  however,  had  been  published  before 


28  THE  ELECTRIC  ARC. 

he  made  the  experiment,  he  tried  the  effect  of  an  arc  and  a 
magnet  on  one  another,  and  found  that  they  deflected  one 
another,  just  as  Arago  and  he  had  predicted.  It  was  on  this 
occasion  that  he  gave  the  name  of  arc  to  the  electric  flame.22 

In  1821  Dr.  Robert  Hare,  a  Professor  in  the  University 
of  Pennsylvania,  published  an  account  of  his  "Galvanic 
Deflagrator,"  an  improved  form  of  battery,  with  which  he 
found  that  he  could  get  much  finer  heating  effects  than  with 
the  older  forms.  His  notions  were  peculiar,  for  he  thought 
that  "the  fluid  extricated  by  Volta's  pile"ivas  "a  compound 
of  caloric  and  electricity,"  both  of  which  were  material  fluids. 
He  remarked  that  "the  igneous  fluid  appeared  to  proceed  from 
the  positive  side,"  which  later  observers  construed  into  his  having 
been  the  first  to  notice  that  material  was  carried  from  the  positive 
to  the  negative  pole.  He  also  said  that,  when  the  positive  pole 
was  of  charcoal  and  the  negative  of  steel,  the  light  was  the  most 
vivid  that  he  had  ever  seen,  and  the  charcoal  assumed  a  pasty 
consistence  as  if  in  a  state  approaching  to  fusion.  He  was  the 
first  to  suggest  that  the  charcoal  could  retain  this  state  with- 
out combining  with  the  air,  and  burning  away,  "because  of 
the  volatilisation  of  the  carbon  forming  about  it  a  circumam- 
bient air."  23 

Silliman  himself,  the  editor  of  the  Journal,  next  obtained  a 
deflagrator  and  made  some  very  notable  discoveries.  It  is  a 
little  difficult  at  first  to  follow  the  course  of  his  observations, 
for  the  poles  of  his  deflagrator  appear  to  have  got  mixed  up ; 
but  he  explained  this  in  a  subsequent  number  of  the  Journal, 
and  even  if  he  had  not  done  so,  in  the  light  of  our  present 
knowledge  there  would  have  been  no  real  possibility  of  mistake. 

He  first  observed  what  must  have  been  a  hissing  arc,  for  he 
described  very  clearly  the  formation  of  a  mushroom  at  the  end 
of  the  negative  charcoal,  and  pointed  out  that  the  negative 
charcoal  grew  in  length  during  the  process,  and  that,  therefore, 
particles  must  be  shot  out  from  the  positive  charcoal  on  to  it. 
To  confirm  this  observation  he  described  and  named  the  crater 
in  the  positive  pole,  and  observed  that,  as  he  moved  the  nega- 
tive over  the  surface  of  the  positive  pole,  it  produced  a  crater- 
shaped  cavity  over  every  place  where  it  rested.  The  first 
notice  of  the  peculiar  smell  of  the  arc  is  also  due  to  him.  "  I 
should  observe  that  during  the  ignition  of  the  charcoal  points, 


A  SHORT  HISTORY  OF  THE  ARC.  29 

there  is  a  peculiar  odour  somewhat  resembling  electricity." 
He  examined  the  negative  charcoal  after  the  arc  was  extin- 
guished, and  found  that  it  appeared  to  have  been  fused  by  the 
heat.24  He  described  the  boiling  bubbles  that  appear  on  both 
carbons  while  the  arc  is  burning,  examined  some  of  these  when 
cold,  and  came  to  the  conclusion  that  they  consisted  of  melted 
carbon.  He  examined  under  the  microscrope  a  mushroom  formed 
between  charcoal  as  the  positive  pole  and  plumbago  as  the 
negative,  and  found  "  a  congeries  of  aggregated  spheres  with 
every  mark  of  perfect  fusion  and  with  a  perfect  metallic  lustre.'* 
These  spheres  were  of  many  colours,  and  some  were  black  and 
some  white.  The  coloured  ones  were  attracted  by  a  magnet, 
proving  that  they  contained  iron.  The  black  ones  he  considered 
to  be  melted  carbon.25  Later  he  fused  two  carbons  together  by 
allowing  them  to  touch  while  an  arc  was  burning  between 
them ;  but  his  experiments  were,  unfortunately,  stopped  by  ill 
health,  and  were  never  resumed.26 

A  great  gap  now  appears  in  the  history  of  the  arc,  and 
there  is  nothing  noteworthy  to  record  till  1838,  when  Gassiot 
showed  that  the  temperature  of  the  positive  electrode  was 
much  greater  than  that  of  the  negative.  Eitter  had  already 
shown  this  for  a  spark,  unless,  perchance,  he  had  an  arc,  which 
is  possible ;  but  Gassiot  showed  that,  of  two  wires  of  the  same 
substance  and  diameter,  that  which  formed  the  positive  pole 
of  a  horizontal  arc  was  melted  so  far  along  as  to  bend  down,, 
while  the  negative  remained  perfectly  stiff.27  In  the  same  year, 


FIQt  14.— Rotation  of  the  Arc  at  the  Pole  of  a  Magnet.     (Copied  from  the 
Transactions  of  the  London  Electrical  Society.) 

in  conjunction  with  Walker,  Sturgeon,   and   Mason,  he  also 
first  observed  the  rotation  of  the  arc  at  the  pole  of  a  magnet. 


30  THE  ELECTRIC  ARC. 

They  found  that  if  they  completed  the  circuit  of  a  powerful 
battery  through  the  pole  of  a  magnet,  so  that  an  arc  was  main- 
tained between  a  wire  from  the  positive  terminal  of  the 
battery  and  this  pole,  then  the  arc  would  rotate — clockwise  if 
the  pole  were  north-seeking,  and  counter-clockwise  if  it  were 
south-seeking.28 

Daniell,  the  inventor  of  the  cell  which  bears  his  name,  made 
many  experiments  with  large  batteries.  Using  charcoal  for  the 
positive  and  platinum  for  the  negative  pole  of  an  arc,  he  found 
that  the  platinum  became  coated  with  carbon,  which  was 
beautifully  moulded  to  its  shape ;  while,  if  he  used  platinum 
for  the  positive  pole  and  charcoal  for  the  negative,  the  latter 
became  covered  with  little  globules  of  platinum  after  the  arc 
was  extinguished.  This  confirmed  Silliman's  discovery  that 
the  material  of  the  positive  pole  was  shot  out  on  to  the 
negative.  Finding  that  with  his  battery  the  arc  would  not 
start  without  actual  contact  of  the  poles,  Daniell  tried 
sending  a  spark  from  a  Leyden  jar  between  the  poles  when 
they  were  apart,  and  succeeded  in  igniting  the  arc  by  this 
means.29 

In  1840  Grove  made  some  very  notable  experiments  to 
determine  whether  the  amount  of  matter  separated  from  the 
poles  by  a  given  quantity  of  electricity  was  constant  for  a  given 
material.  He  came  to  the  conclusion  that  it  was,  and  that 
"  the  all-important  law  of  Faraday  is  capable  of  much  exten- 
sion." The  law  he  alluded  to  was,  of  course,  the  law  of  elec- 
trolysis, and  shows  that  he  considered  the  action  of  the  arc  to 
be  purely  electrolytic.  Indeed,  in  the  Paper  in  which  he 
described  these  experiments  he  said,  "The  passage  of  the 
current  is,  as  proved  in  these  experiments,  materially  modified 
by  the  nature  of  the  elastic  medium  through  which  it  passes, 
.and  is  greatly  aided  when  such  medium  is  capable  of  uniting 
chemically  with  the  electrodes.  In  pure  hydrogen  I  have  never 
yet  been  able  to  maintain  a  continuous  arc,  except  with  char- 
coal, which  forms  carburetted  hydrogen."  Grove  tried  using 
the  carbon  from  gas  retorts,  but  found  that  charcoal  gave  a 
larger  and  more  diffuse  flame.  He  described  the  three  requi- 
sites for  a  brilliant  discharge  in  an  oxydating  medium  as  being 
oxydability,  volatility,  and  looseness  of  aggregation  of  the 
,  particles.80 


A  SHORT  HISTORY  OF  THE  ARC.  31 

To  Becquerel  is  due  the  honour  of  having  discovered  that  the 
electric  light  had  the  same  chemical  effect  on  the  salts  of  silver 
as  sunlight,31  and  De  la  Rive  first  used  this  power  of  the  arc 
to  obtain  a  daguerrotype,  a  faint  one  it  is  true,  of  a  bust.32 

In  the  same  year  Mackrell  obtained  an  arc  between  two  fine 
iron  wires  in  dilute  sulphuric  acid,  and  he  found  that,  if  he  used 
a  positive  pole  of  iron  and  a  negative  one  of  charcoal,  if  the 
iron  were  put  into  the  acid  first  the  charcoal  became  brilliant, 
but  if  the  charcoal  were  immersed  first,  no  such  result  took 
place.34 

Casselmann,  in  1844,  first  described  the  shape  of  a  long  arc, 
as  two  cones  with  their  bases  in  contact  with  the  carbons,  and 
their  points  touching  one  another.  He  allowed  the  arc  to  burn 
away  till  it  became  extinguished,  under  different  conditions, 
and  found  that  with  the  same  battery  a  longer  arc  could  be 
maintained  between  charcoal  electrodes  than  between  electrodes 
of  carbon  prepared  as  the  plates  of  a  Bunsen  battery  are  pre- 
pared. Between  these  carbons  also  the  arc  hissed,  but  if  they 
were  heated  red  hot  beforehand,  and  steeped  in  solutions  of 
such  volatile  substances  as  sodium  or  potassium,  the  arc  burnt 
quietly  and  steadily,  and  would  grow  to  a  greater  length  before 
it  became  extinguished.35 

In  1845  a  very  curious  discovery  was  made  by  Neef,  who  wished 
to  find  out  at  which  part  of  the  arc  the  light  first  appeared. 
In  order  to  eliminate  any  secondary  heating  effect  produced  by 
the  combination  of  the  hot  positive  pole  with  the  oxygen  of  the 
air,  he  used  platinum  poles — a  plane  for  the  positive  and  the 
point  of  a  cone  for  the  negative.  Between  these  he  struck  an 
arc  with  a  very  small  current  by  means  of  a  spark  from  a 
Ley  den  jar.  He  then  observed  the  effect  with  a  microscope, 
and  found  that  the  light  started  at  the  negative  pole,  with  no 
perceptible  heat.  The  results  he  considered  he  obtained  were 
the  following : — 

(1)  The  light  always  appears  first  at  the  negative  pole,  and 
this  first  light  is  independent  of  combustion. 

(2)  The  source  of  the  heat  is  the  positive  pole,  and  this  heat 
is  originally  dark  heat. 

(3)  The  light  and  heat  do  not,  at  first,  mingle,  but  only 
when  they  have  attained  a  certain  intensity ;  from  this  fusion 
the  phenomena  of  combustion  and  the  flame  are  produced. 


32  THE  ELECTEIG  ARC. 

He  was  the  first  to  suggest  that  the  carbon  which  was  fused 
and  shot  off  from  the  positive  pole  was  condensed  at  the 
negative  pole  to  the  specific  gravity  of  crystallisable  gra- 
phite.37 

De  la  Rive,  after  having  made  the  first  daguerreotype  with 
the  arc,  made  a  series  of  experiments  as  to  the  longest  arc  that 
could  be  maintained  by  a  given  battery  when  the  poles  were 
of  various  substances.  He  used  a  voltameter  to  measure  the 
current,  and  found  that  the  current  that  was  flowing  when  the 
arc  became  extinguished  was  the  same  for  all  substances,  but 
that  the  length  of  the  arc  varied  with  the  substance.  He 
noticed  that  when  he  had  a  slab  of  carbon  for  the  negative  pole 
and  a  pointed  carbon  rod  for  the  positive,  the  deposit  from  the 
positive  took  a  regular  form.  Also  the  longest  arc  was  only 
half  as  long  with  this  arrangement  as  it  was  when  the  positions 
of  the  slab  and  the  rod  were  reversed.  When  the  poles  were 
of  magnetised  iron  the  longest  arc  was  much  shorter  than  when 
the  iron  poles  were  unmagnetised.38 

In  the  same  year  Van  Breda,  experimenting  on  the  arc  in 
vacuo,  found  that  with  copper  poles,  when  he  placed  a  slip  of 
iron  in  the  arc  between  them,  the  copper  of  both  poles  became 
covered  with  iron,  and  there  were  traces  of  copper  on  the  iron 
slip.  On  weighing  both  electrodes  and  the  iron  slip,  he  found 
that  the  electrodes  had  each  gained  in  weight,  and  the  iron 
lost,  but  that  taking  all  three  together  there  had  been  a  loss 
of  weight.  With  one  electrode  of  iron  and  one  of  coke,  the 
iron  lost  more  weight  than  the  coke,  whether  it  was  at  the 
positive  or  negative  pole.39 

Matteucci  made  some  very  accurate  and  important  experi- 
ments on  the  amount  of  matter  lost  by  each  electrode  in  a 
given  time.  Like  Van  Breda,  he  came  to  the  conclusion  that 
matter  was  shot  out  by  both  poles,  and  he  pointed  out  that 
the  two  sets  of  particles,  being  in  opposite  electric  states,  must 
attract  one  another.  He  found  that  the  difference  of  tempera- 
ture between  the  poles  was  greater  the  smaller  the  conductivity 
of  the  electrodes,  and  that  the  amount  of  matter  lost  by  each 
depended  upon  its  temperature,  its  oxydability,  and  the  vola- 
tility and  fusibility  of  the  products  of  oxydation.  Both  poles 
lost  more  in  air  than  in  a  vacuum  in  a  given  time.  With  coke 
electrodes  he  estimated  that  the  proportion  of  the  loss  at  the 


A  SHORT  HISTORY  OF  THE  ARC.  33 

positive  pole  to  that  at  the  negative  varied  between  2  to  1  and 
5  to  1,  according  to  the  length  of  the  arc.40 

Quet,  placing  a  vertical  carbon  arc  perpendicular  to  the 
common  axis  of  the  coils  of  an  electromagnet,  found  that  the 
arc  shot  out  horizontally,  like  the  flame  of  a  blow-pipe,  and 
that,  unless  the  carbons  were  very  close  together,  the  arc 
became  extinguished  with  a  loud  noise.41  Several  electric  blow- 
pipes on  this  principle  have  since  been  invented. 

In  1852  Grove  made  a  most  interesting  experiment,  which 
showed  that  a  liquid  could  act  as  one  pole  of  an  arc.  He 
attached  fine  platinum  wires  to  the  terminals  of  a  battery  of  500 
cells,  dipped  the  ends  of  both  wires  into  distilled  water,  and  then 
gradually  withdrew  the  negative  wire  till  it  was  a  quarter  of 
an  inch  above  the  surface  of  the  water.  "  A  cone  of  blue  flame 
was  now  perceptible,  the  water  forming  its  base,  and  the  point 
of  the  wire  its  apex.  The  wire  rapidly  fused,  and  became  so 
brilliant  that  the  cone  of  flame  could  no  longer  be  perceived, 
and  the  globule  of  fused  platinum  was  apparently  suspended  in 
air,  and  hanging  from  the  wire ;  it  appeared  sustained  by  a 
repulsive  action,  like  a  cork  ball  on  a  jet  d'eau,  and  threw  out 
scintillations  in  a  direction  away  from  the  water.  The  surface 
of  the  water  at  the  base  of  the  cone  was  depressed  and  divided 
into  little  concave  cups,  which  were  in  a  continual  agitation." 
When  the  conditions  were  reversed,  so  that  the  negative  wire 
was  immersed  and  the  positive  out  of  the  water,  the  effect  was 
the  same,  but  not  so  marked.  The  cone  was  smaller,  and  its 
base  was  much  narrower  in  proportion  to  its  height.42 

The  first  accurate  quantitative  experiments  on  the  arc  were 
made  by  Edlund  in  1867.  In  spite  of  the  disadvantages  under 
which  he  laboured — for  he  had  no  dynamo,  and  at  that  time 
there  were  no  recognised  units  of  current,  P.D.,  or  resistance — 
Edlund  discovered  one  of  the  fundamental  conditions  of  the  arc, 
namely,  that  with  a  constant  current  the  apparent  resistance  is 
equal  to  a  constant  resistance,  plus  a  resistance  which  varies 
directly  with  the  length  of  the  arc. 

Edlund's  method  of  experimenting  was  as  follows :  He  used 
a  battery  to  send  a  current  through  an  arc  of  definite  length, 
then,  putting  out  the  arc  and  pressing  the  carbons  tightly 
together,  he  measured  the  distance  by  which  he  had  to  separate 
the  plates  in  a  copper  voltameter  so  as  to  bring  the  current  to 

21 


34  THE  ELECTRIC  ARC. 

the  same  value  as  before.  Doing  this  for  various  lengths  of  arc 
he  found  that,  as  long  as  the  current  was  kept  constant,  the  length 
of  the  copper  voltameter  which  represented  the  arc  could  be 
expressed  by  a  constant  length  plus  a  length  which  varied 
directly  with  that  of  the  arc. 

Hence,   putting  his  result  in  the  form  of  an  equation,  he 
found  out  that 


where  r  is  the  apparent  resistance  of  the  arc,  I  its  length,  and  a 
and  b  constants  for  a  constant  current. 

When,  however,  the  current  was  varied,  he  found  that  a  and  b 
both  diminished  as  the  current  increased,  so  that  the  apparent 
resistance  of  the  arc  for  a  given  length  was  smaller  the  greater 
the  current.  The  numbers  which  he  obtained  for  a  justified 
him,  he  considered,  in  concluding  that  a  varied  inversely  as  the 
current,  but  those  for  b  were  too  small  to  enable  him  to  arrive 
at  the  law  connecting  b  with  the  current. 

Edlund  started  his  experiments  with  the  idea  that  there 
was  a  back  E.M.F.  in  the  arc  caused  by  the  disintegration  of 
the  carbon  particles,  and  therefore,  having  obtained  several 
values  of  a  and  b  with  different  currents,  he  calculated  the 
back  E.M.F.  in  the  arc  when  each  of  those  currents  was 
flowing. 

From  these  calculations  he  concluded  that  the  back  E.M.F. 
in  the  arc  had  a  constant  value  equal  to  that  of  about  23  Bunsen's 
cells,  for  all  the  currents  he  used,  and  that  the  true  resistance  of  the 
arc  was  directly  proportional  to  its  length,  increasing,  however,  as 
the  current  decreased. 

He  next  considered  the  question  theoretically,  and  gave 
what  he  regarded  as  a  proof  that  the  back  E.M.F.  in  the  arc 
must  be  independent  of  the  current,  and  also  that  the  work 
performed  in  the  arc  by  the  current  was  proportional  to  the 
current  as  long  as  the  E.M.F.  of  the  battery  remained 
constant. 

He  then  made  a  new  series  of  experiments  to  determine 
whether  the  back  E.M.F.  depended  upon  the  E.M.F.  of  the 
battery  used  to  produce  the  current,  and  decided  that  it  did 
not.44 

Edlund's  next  series  of  experiments  was  undertaken  to 
find  out  whether  the  back  E.M.F.  was  constant  with  smaller 


A  SHORT  HISTORY  OF  THE  ARC.  35 

currents  than  had  been  employed  in  the  first  series.  The  deflec- 
tions produced  by  the  currents  in  the  tangent  galvanometer  used 
were  not  published  in  this  case,  as  they  had  been  before;  but 
Edlund  considered  that  his  results  showed  that,  in  the  case  of 
small  currents,  the  back  KM.F.  diminished  as  the  current  was 
decreased.  He  used  copper,  brass,  and  silver  pole  points  for 
these  experiments,  as  well  as  carbon.45 

Edlund's  third  series  of  experiments  was  very  striking.  He 
found  that,  when  an  arc  was  produced  with  a  somewhat  large 
current  between  carbon  poles,  the  arc  continued  for  a  short 
time  after  the  circuit  was  broken,  so  that,  if  the  circuit  were 
closed  again  fairly  quickly  after  the  break  had  been  made,  the 
arc  was  not  put  out.  But,  on  the  other  hand,  when  silver  poles 
were  used,  the  arc  did  not  continue  for  even  one-eightieth  of  a 
second  after  the  circuit  was  broken. 

From  this  he  concluded  that  if  carbon  poles  were  used,  and 
if  immediately  after  breaking  the  circuit  the  carbons  were 
switched  on  to  a  galvanometer,  a  momentary  current  would  be 
sent  by  the  arc  through  the  gal  variometer,  and  the  existence  of  the 
•back  E.M.F.  in  the  arc  would  thus  be  made  certain.  A  series  of 
experiments  carried  out  in  this  way,  with  and  without  a  battery 
being  switched  with  the  arc  into  the  galvanometer  circuit, 
led  Edlund  to  conclude  that  the  back  E.M.F.  existing  in  the 
arc  after  the  main  circuit  had  been  broken  could  not  be  less 
than  that  of  from  10  to  15  Bunsen's  cells.  Further,  from'  the 
momentary  current  being  increased  when  the  negative  carbon 
was  warmed  by  a  Bunsen's  burner,  and  not  diminished  as  might 
have  been  expected  had  the  back  E.M.F.  been  a  thermo- 
electric one  (set  up  by  the  positive  carbon  being  hotter  than 
the  negative),  he  concluded  that  the  back  E.M.F.  in  the  arc 
was  not  due  to  thermo-electric  action.46 

In  1876  the  Jablochkoff  candle  came  into  use.  It  consisted 
of  two  upright  parallel  carbon  rods,  separated  from  one  another 
by  a  layer  of  solid  insulating  material,  which  burnt  away  at 
about  the  same  rate  as  the  carbons.  This  solid  material  was 
supposed  to  be  necessary  to  keep  the  arc  from  running  down 
the  carbons  and  burning  anywhere  but  at  the  tips. 

When,  later,  it  was  discovered  that  the  arc  still  remained  at 
the  ends  of  the  carbon,  even  when  there  was  nothing  but  air 
between  them,  this  was  attributed  to  the  action  of  the  upward 

P2 


36 


THE  ELECTEIC  AEG. 


current  of  hot  air  and  vapour.  In  1878,  however,  Prof.  Ayrtort 
gave  the  true  explanation,  and  proved  that  the  hot-air  theory 
could  not  be  correct,  by  showing  that  the  arc  remained  at  the 
ends  of  the  carbons,  even  when  they  were  held  upside  down. 
He  pointed  out  that  in  remaining  always  at  the  ends  of  the 
carbons  the  arc  was  simply  following  Ampere's  law  concerning 
the  tendency  of  a  circuit  in  which  a  current  is  flowing  to 
enlarge  itself,  on  account  of  the  repulsive  action  of  the  current 
in  one  part  of  the  circuit  on  the  current  in  another  part  at 
right  angles  to  it.  Prof.  Ayrton's  own  explanation  will  make 
this  clearer. 

"  The  figure  below,  in  which  the  continuous  arrows  indicate 
the  directions  of  the  currents,  and  the  dotted  arrows  the  line  of 
action  of  the  repulsive  forces,  show  this  action  clearly.  The 
carbons  are  placed  further  apart  in  the  figure  than  they  are  in 
reality,  merely  for  convenience  of  drawing.  The  two  forces  are 


r\ 


ARC    r\ 


MACHINE 

FIG.  15. 


oblique  to  the  carbons  ;  but  the  resultant  is  parallel  to  them,, 
and  will  always  be  away  from  those  ends  of  the  carbons  which 
are  connected  with  the  magneto-electric  machine,  no  matter 
how  often  the  whole  current  be  reversed."  49 

This  explanation  also  applies  to  the  form  taken  by  a  hori- 
zontal arc,  and  shows  that  the  upward  direction  of  Sir  Hum- 
phry Davy's  long  arc  (see  Fig.  13,  p.  27)  depended  principally 
on  the  position  of  the  poles  relatively  to  the  remainder  of  the 
circuit.  The  same  cause  makes  the  vertical  arc,  when  it  is- 
long  and  the  current  is  small,  take  up  a  position  between 
the  points  of  the  carbon  which  are  farthest  from  each  other, 
and  thus  make  itself  as  long  as  possible. 

Mr.  Schwendler,  during  the  course  of  an  investigation  or* 
"  The  Electric  Light,"  carried  out  in  1878  for  the  Board  of 


A  SHORT  HISTORY  OF  THE  ARC.  37 

Directors  of    the    East    Indian  Railway   Company,    gave  the 

following  conclusions  in  a  precis  of  his  report : 

"  There  appears  to  be  no  doubt  that  an  appreciable  E.M.F. 
in  the  arc  is  established,  which  acts  in  opposition  to  the  E.M.F. 
of  the  dynamo  machine.  This  E.M.F.  of  the  arc  increases 
with  the  current  passing  through  the  arc.  The  resistance  of 
the  arc  for  constant  length  is  also  a  function  of  the  current 
passing  through  it,  i.e.,  the  resistance  of  the  arc  decreases  with 
the  current  (see  the  following  table)." 

Table  I.  (Schwendler). 


Current  in 

Resistance  of  the  arc 

E.M.F.  of  the  arc 

webers. 

in  Siemens  units. 

in  volts. 

28-81 

0-91 

2-02 

23-87 

1-72 

1-91 

16-27 

1-97 

186 

Mr.  Schwendler  said,  further,  that  he  considered  it  highly 
probable  that  the  resistance  of  an  arc  of  constant  length  was 
inversely  proportional  to  the  current.  No  details  were  given  in 
this  precis  regarding  the  way  in  which  the  E.M.F.  of  the  arc 
was  measured.50 

In  1879  Messrs.  De  la  Rue  and  Hugo  Miiller,  while  experi- 
menting on  the  discharge  in  vacuum  tubes,  came  to  the  con- 
clusion that  "  the  stratified  discharge  in  a  vacuum  tube  is 
simply  a  magnified  form  of  arc."  In  order  to  test  this  theory 
they  made  a  series  of  experiments  on  discharges  in  various 
gases  at  various  pressures,  with  the  poles  at  various  distances 
from  one  another,  and  of  different  shapes.  The  poles  were 
-fixed  in  a  bell  jar  that  could  be  filled  with  the  different  gases 
and  exhausted ;  a  suitable  arrangement  was  made  for  altering 
the  distance  between  the  poles,  and  the  gases  used  were  air, 
hydrogen  and  carbonic  acid. 

In  air  the  pressures  varied  from  2 '6mm.  to  761mm.,  the  dis- 
tances varied  between  0'54in.  and  6  4in.,  the  current  ranged 
from  0-01390  to  0-04474  webers,  and  the  number  of  chloride 
of  silver  cells  used  varied  from  10,940  to  11,000.  The  sub- 
stance of  the  electrodes  was  only  definitely  mentioned  in  one 
case,  when  it  was  brass.  Many  beautiful  engravings,  showing 
the  appearance  of  the  discharge  under  different  circumstances, 


38  THE  ELECTRIC  ARC. 

were  published ;  from  these  it  appeared  that  in  air  the  light 
usually  divided  itself  into  at  least  two  and  sometimes  more 
parts,  with  dark  spaces  between  them. 

In  hydrogen,  in  some  cases,  the  discharge  showed  a  very- 
definite  stratification.  In  carbonic  acid,  when  the  pressure 
was  very  small,  there  was  very  little  evidence  of  stratification  ; 
but  in  both  gases  the  discharge  was  divided,  as  in  air,  into 
light  and  dark  parts. 

Mr.  Seaton,  one  of  the  assistants  of  Messrs.  De  la  Rue  and 
Miiller,  first  noticed  a  very  interesting  circumstance  connected 
with  the  discharge.  Whenever  contact  was  first  made  the 
pressure  in  the  bell  jar  increased  far  more  than  could  be 
accounted  for  by  the  rise  of  temperature  of  the  enclosed  gas. 
The  moment  contact  was  broken  the  pressure  fell  almost  to 
what  it  had  been  before  contact  was  made,  the  slight  increase 
being  due  to  rise  of  temperature.  It  was  found  by  experiment 
that  the  increase  of  pressure  took  place  at  both  terminals 
equally.  The  experimenters  considered  it  to  be  accounted  for 
by  uihe  projection  of  the  gas-molecules  by  electrificatioi> 
against  the  walls  of  the  glass  vessel,  producing  thereby  effects 
of  pressure,  which,  however,  are  distinct  from  the  molecular 
motion  induced  by  heat." 

The  parts  of  the  Paper  which  concern  the  arc  are  summed 
up  in  the  following  manner  : — 

"When  the  discharge  takes  place  there  is  a  sudden  dilata- 
tion of  the  medium,  in  addition  to  and  distinct  from  that 
caused  by  heat.  This  dilatation  ceases  instantaneously  when 
the  discharge  ceases. 

"  The  electric  arc  and  the  stratified  discharge  in  vacuum, 
tubes  are  modifications  of  the  same  phenomenon."53 

In  the  same  year  Rossetti  found,  from  a  large  number  of 
experiments,  that  the  maximum  temperature  of  the  positive 
pole  was  3,900°C.,  and  that  of  the  negative  about  3,150°C. 
The  temperature  of  the  arc  itself  he  found  to  be  about  4,800°C. 
whatever  the  intensity  of  the  current  flowing.  The  method  of 
experimenting  was  not  given.54 

In  the  following  year,  1880,  the  first  measurements  of  the 
diameter  of  the  crater  of  the  positive  carbon  were  made  by  Mr. 
J.  D.  F.  Andrews,  who  was  also  the  first  to  remark  that,  in 
order  that  a  definite  result  might  be  obtained  with  each  current 


A  SHORT  HISTORY  OF  THE  ARC. 


39 


and  length  of  arc  employed,  the  arc  should  be  allowed  to  burn 
steadily  and  quietly  for  at  least  half  an  hour  before  any 
measurements  were  taken. 

He  measured  the  diameter  of  the  crater,  when  cold,  with  a 
rule  divided  into  lOOths  of  an  inch,  and,  neglecting  its  depth, 
which  was  very  small  with  the  length  of  arc  he  used 
(TVn.),  he  found  the  area  from  the  diameter.  He  considered 
that  his  experiments  showed  that  the  area  of  the  crater  was 
"  directly  proportional  to  the  quantity  of  current  producing  it." 
In  proof  of  this  he  gave  the  following  table  : — 

Table  II.  (Andrews). — Comparison  of  Observed  Currents  and 
Currents  calculated  on  the  Assumption  that  Area  of  Crater  is 
directly  proportional  to  Current. 


Diameters  of 
craters,  in 
inches. 

Areas  of  craters, 
in  inches. 

Quantities  of 
cur.  in  webers 
measured. 

Quantities  of 
current  in  webers 
cal.  from  craters. 

0140 
0-156 
0-186 
0-203 
0-266 
0-326 
0-453 

0-0196 
0-0243 
0-0272 
0-0324 
0-0556 
0-0825 
0-1602 

9 
12 

29 
42 
81 

9-9 
12-4 
13-8 
16-5 
28-3 
42-0 
81-6 

The  diameters  of  the  carbons  used  were  not  given. 

Mr.  Andrews  remarked  that  when  the  arc  hissed  the  end  of 
the  positive  carbon  was  covered  with  a  number  of  small  craters, 
showing  that  it  moved  about,  and  that  a  number  of  very  small 
arcs  appeared  to  try  to  spread  over  the  end  of  the  positive  car- 
bon, each  detonating  the  air,  and  thus  causing  a  hissing  noise.55 

Le  Roux  considered  that  the  great  fall  of  potential  at  the 
positive  carbon  was  caused  by  a  back  E.M.F.,  the  result  of  a 
thermo-electric  effect.  His  idea  was  that  the  carbon  of  the 
positive  electrode  was  electro-positive  to  the  vapour  of  the  arc 
in  a  degree  which  increased  as  the  temperature  increased.  He 
found  that  with  a  high  resistance  galvanometer  in  the  arc  circuit 
he  could  detect  the  back  E.M.F.  0'2sec.  after  he  had  stopped 
the  arc  by  hand.57 

Niaudet  in  1881  first  noticed  that  the  hissing  of  the  arc  was 
accompanied  by  a  sudden  fall  of  P.D.,  and  gave  the  following 
table  of  observations  that  he  had  made : — 


40  THE  ELECTRIC  ARC. 

Table  III.  (Niaudet). — Currents  and  P.D.  with  Silent  and 
Hissinq  Arcs.58 


Current  in  webers. 

P.D.  (presumably  in  volts). 



34 
36 
34 
43 
38-1 

54-3 
43 
49 
41-4 
49 

Silent 
Hissing 
Silent 
Hissing 
Silent 

In  a  Paper  on  "  The  Resistance  of  the  Electric  Arc  "  Profs. 
Ayrton  and  Perry  in  1882  described  experiments  made  with 
Grove's  cells  to  test  the  accuracy  of  Mr.  Schwendler's  conclusions 
concerning  the  back  E.M.F.  and  the  resistance  of  the  arc, 
and  they  found  that,  when  carbons  0'24in.  in  diameter  were 
used  and  the  length  of  the  arc  kept  constant,  the  current  could 
be  varied  from  about  5  to  15  amperes  without  much  change 
being  produced  in  the  P.D.  between  the  carbons.  They  also 
used  a  Brush  machine  to  produce  an  arc  up  to  l'25in.  in  length, 
and  gave  as  the  equation  connecting  V,  the  P.D.  between  the 
carbons  in  volts,  and  a,  the  length  of  the  arc  in  inches 
V  =  63  +  55a-63xlO-10a, 

and  this  equation  they  regarded  as  being  true  for  currents 
between  5-5  and  1CK  amperes  with  the  carbons  employed.59 

In  1882  Prof.  Dewar  made  some  very  interesting  experi- 
ments on  the  internal  pressure  of  the  arc.  He  used  a  horizontal 
arc  maintained  between  carbon  tubes,  each  of  which  was 
attached  to  a  manometer.  With  a  steady  silent  arc  the  mano- 
meter attached  to  the  positive  carbon  showed  a  fixed  increase 
of  pressure  of  about  1mm.  to  2mm.  of  vertical  water  pressure, 
while  at  the  negative  carbon  there  was  a  slight  diminution  of 
pressure.  The  same  results  were  obtained  when  the  arc  and 
ends  of  the  carbons  were  enclosed  in  a  block  of  magnesia  to 
equalise  the  temperature  of  the  poles,  and  also  when  the  mano- 
meters were  filled  with  carbonic  oxide  or  nitrogen  instead  of 
with  air. 

When  the  arc  hissed,  it  often  no  longer  covered  the  ends  of 
the  carbons,  so  that  the  manometers  showed  no  pressure  ;  but 
when  this  did  not  happen,  the  positive  carbon  showed  a  dimi- 
nution and  the  negative  an  increase  of  pressure  with  a  hissing 
arc. 


A  SHORT  HISTOIiY  OF  THE  AUG.  41 

From  these  experiments  Prof.  Dawar  concluded  that  the  arc 
acted  as  if  it  had  a  surface  tension.60 

In  1883  Frolich,  desiring  to  find  out  whether  Edlund's  equa- 
tion r  =  a  +  bl  were  true  for  the  larger  currents  that  could 
be  obtained  with  dynamos,  used  the  results  of  experiments  made 
for  the  purpose  of  testing  the  dynamos  constructed  by  Messrs. 
Siemens  and  Halske,  by  various  people  at  various  times,  to 
obtain  an  equation  connecting  the  P.D.  between  the  carbons 
with  the  length  of  the  arc.  In  the  table  given  in  his  Paper 
the  P.D.s  corresponding  with  different  currents  for  the  same 
length  of  arc  showed  wide  variations,  yet  he  took  it  for  granted 
that  the  P.D.  was  really  independent  of  the  current,  and  so  he 
deduced  the  equation 


as  the  relation  that  would  connect  the  P.D.  between  the  carbons 
with  the  length  of  the  arc,  where  a  and  b  were  the  same, 
whatever  the  current,  if  there  were  no  errors  of  observation  in 
the  experiments. 

Frolich  found  what  he  considered  to  be  the  numerical  values 
of  a  and  5,  and  so  he  put  his  equation  connecting  V.  the  P.D. 
in  volts  between  the  carbons  with  I  the  length  of  the  arc  in 
millimetres  in  the  form 


From  this  formula  he  calculated  what  he  considered  ought 
to  have  been  the  P.D.s  for  the  various  currents  and  lengths  of 
arc  with  any  current  from  1  to  100  amperes,  in  the  47  measure- 
ments the  results  of  which  he  quoted;  and  the  differences 
between  the  results  given  by  his  formula  and  by  experiment 
he  put  down  to  errors  of  observation. 

By  dividing  by  A,  the  current  in  amperes,  Frolich's  formula 
became 

39     1-81 


and  this  he  considered  was  the  formula  which  gave  r  the  appa- 
rent resistance  in  ohms  of  an  arc  I  millimetres  long  produced  by 
a  current  of  A  amperes.  He  used  the  latter  formula  to  calculate 
a  table  of  273  apparent  resistances  of  arcs,  varying  from  Omm. 
to  20mm.  in  length,  and  produced  by  currents  of  1,  5,  10,  15,  <fec., 


42  THE  ELECTRIC  ARC. 

up  to  100  amperes;  but  no  experiments  were  adduced  giving 
results  agreeing  with  his  calculated  values. 

He  then  proceeded  to  inquire  if  his  "newly-discovered 
facts  "  threw  any  light  upon  the  question  whether  there  was  a 
back  E.M.F.  in  the  arc,  or  merely  a  contact  resistance,  and  he 
concluded  that  either  explanation  was  consistent  with  the  facts, 
provided  that  the  cross-section  of  the  arc  was  directly  propor- 
tional to  the  current,  which  he  considered  likely. 

Multiplying  both  sides  of  his  equation  by  A,  he  obtained  the 
following  equation,  giving  W,  the  power  in  watts  expended  in 
the  arc : — 

W  =  (a  +  H)A; 

and  he  concluded  from  this  equation  that  the  power  expended  in 
an  arc  of  fixed  length  was  directly  proportional  to  the  current.61 

In  1885  Peukert  published  an  account  of  some  experi- 
ments he  had  made  with  constant  currents  and  varying 
lengths  of  arc,  for  the  purpose,  as  he  said,  of  "  eliminating  one 
of  the  three  possible  variables,  P.D.  current,  and  length  of  arc. " 
In  order  to  avoid  having  a  crater,  and  thus  complicating  the 
measurement  of  the  length  of  the  arc,  which  was  made  by 
projecting  the  distance  between  the  carbons  on  to  a  millimetre 
scale,  he  had  the  carbons  filed  flat  before  each  experiment,  and 
the  determination  made  before  the  carbons  had  had  time  to 
burn  away  much. 

Having  obtained  the  P.D.s  needed  to  send  currents  of  10, 
15,  20,  25  and  30  amperes  through  various  lengths  of  arc, 
he  plotted  curves  connecting  the  apparent  resistance  with  the 
length  of  the  arc  for  each  current,  and  found  that  they  were 
all  straight  lines,  so  that  Edlund's  equation, 

r  =  a-{-  bl, 

was  proved  true  for  large  as  well  as  for  small  currents. 

Peukert,  like  Edlund,  found  that  a  varied  inversely  as  the 
current,  but  he  pointed  out  that  b  diminished  more  quickly 
than  the  current  increased.  This  latter  fact,  he  thought,  was 
partly  explained  by  the  air  surrounding  the  arc  becoming  very 
hot  when  the  current  was  large,  and  so  acting  itself  as  a 
conductor. 

He  considered  the  question  of  a  back  E.M.F.  in  the  arc,  and 
showed  that  the  mean  value  of  A  a  in  his  experiments  was  about 


A  SEOET  HISTOEY  OF  THE  ARC.  43 

35  volts.  He  thought,  however,  that  an  E.M.F.  of  this  large 
value  could  not  be  set  up  by  the  disintegration  of  the  carbon,  as 
Edlundhad  supposed,  and  that  aback  E.M.F.,  if  so  produced, 
ought  to  increase  with  the  current.  He  also  considered  the 
possibility  of  the  back  E.M.F.  being  produced  thermo-electrically, 
or  by  the  combination  of  the  carbon  points  with  the  hydrogen 
gas  liberated  by  decomposition  of  vapour  in  the  air,  but  both 
these  suggestions  he  rejected  also. 

Peukert  finally  concluded  that  most  probably  the  resistance 
of  the  arc  was  really  composed  of  two  parts,  one  that  of  the 
arc  proper,  while  the  other,  and  much  the  larger  part,  was  a 
mechanical,  or  contact,  resistance  between  the  arc  and  the 
carbon.  And  he  added  that  a  certain  minimum  P.D.  being 


FIG.  16. 


necessary  to  maintain  an  arc,  which  fact  had  been  adduced  as 
a  proof  of  the  existence  of  a  back  E  M.F.,  might  arise  from  a 
certain  P.D.  being  necessary  to  tear  off  the  carbon  which 
formed  the  conducting  medium  between  the  two  carbons.62 

In  1885  Von  Lang  endeavoured  to  measure  the  true  resistance 
of  the  arc,  as  distinguished  from  the  apparent  resistance,  which 
alone  had  been  determined  by  previous  experimenters.  To  do 
this  he  used  a  battery,  B^  (Fig.  16),  to  produce  two  arcs 
1^  and  L2,  in  series,  each  Jmm.  long,  formed  with  carbons  5mm. 
in  diameter;  and  between  the  arcs  there  was  placed  a  resistance, 
11 R.  A  point,  A,  in  the  Resistance  was  then  found,  having  the 


44  THE  ELECT  ETC  AliC. 

same  potential  as  B,  the  middle  point  of  the  battery.  Then, 
since  these  two  points  of  the  quadrilateral  were  at  the  same 
potential,  the  parallel  resistance  of  the  two  halves  of  the 
quadrilateral  between  A  and  B  could  be  measured  with  a 
Wheatstone's  bridge,  exactly  as  if  there  were  no  E.M.F.s  in  the 
quadrilateral. 

This  resistance  Von  Lang  found  to  be  1*82  ohms,  and  there- 
fore the  resistance  right  round  the  quadrilateral  was  4  x  T82, 
or  7*28  ohms.  Next  the  arcs  were  replaced  by  equal  resis- 
tances of  such  a  value  that  the  current  flowing  round  the 
quadrilateral,  as  measured  by  the  ammeter,  C,  was  the  same  as 
before,  viz.,  4*32  amperes.  The  parallel  resistance  between  the 
points  A  and  B  was  now  found  to  be  6*29  ohms,  and  con- 
sequently the  resistance  right  round  the  quadrilateral  was 
4x6-29,  or  25-16  ohms.  Hence  the  E.M.F.  of  the  battery. 
BiBgWas  4-32x25-16,  or  108-7  volts.  And,  as  the  quadri- 
lateral had  a  resistance  of  7'28  ohms  when  the  two  arcs  were  in 
the  circuit,  a  P.D.  of  4'32  x  7'28,  or  31-4  volts,  must  have  been 
employed  in  sending  the  current  of  4'32  amperes  round  this 
quadrilateral  as  far  as  its  resistance  was  concerned.  Con- 
sequently a  P.D.  of  108-7-31-4,  or  77'3  volts,  must  have 
been  employed  in  overcoming  the  back  E.M.F.  of  the  two  arcs, 
or  the  back  E.M.F.  of  each  arc,  was  38 -6  volts.63 

Stenger  in  1885  made  some  experiments  in  order  to  confirm 
the  conclusion  come  to  by  De  la  Rue  and  Miiller  (see  p.  37), 
that  there  is  no  sharp  distinction  between  an  arc  and  the 
discharge  in  a  vacuum  tube,  and  also  to  find  out  what  are  the 
conditions  that  tend  to  make  the  discharge  take  one  form  rather 
than  the  other,  when  the  current  is  passed  through  electrodes 
in  a  vacuum,  and  under  what  conditions  the  two  sorts  of 
discharge  may  merge  into  one  another. 

He  considered  that  they  were  distinguished  from  one  another 
in  four  ways  : — 

(1).  The  gaseous  portion  has  less  resistance  in  the  arc  than 
in  the  tube  discharge. 

(2).  In  the  arc  the  anode  is  hotter  than  the  cathode,  in  the 
tube  discharge  the  reverse  is  the  case. 

(3).  In  the  spectrum  of  the  arc  the  light  of  the  substance  of 
the  electrodes  predominates  over  that  of  the  vapour  between 
them,  while  in  the  tube  discharge  the  spectrum  only  gives  the 


A  SHORT  .HISTORY  OF  THE  ARC.  45. 

lines  of  the  gas  and  is  independent   of    the    nature    of   the 
electrodes. 

(4).  In  the  arc  both  electrodes  waste  away,  in  the  tube 
discharge  only  the  cathode  does  so. 

As  regarded  the  first  two  distinctions,  he  quoted  Hittorf  to 
show  that  the  resistance  in  a  vacuum  tube  diminished  as  the 
pressure  increased.  When  contact  was  made  with  a  tube  of 
nitrogen  at  a  pressure  of  17mm.,  the  current  was  extremely 
small,  and  the  cathode  was  hotter  than  the  anode.  When  the 
pressure  was  raised  to  53mm.  and  all  the  other  conditions  were 
the  same,  the  resistance  diminished  so  much  that  the  current 
increased  to  two  amperes,  "  a  strength  that  might  be  used  for 
an  arc"  as  Stenger  said,  and  the  anode  became  hotter  than  the 
cathode. 

He  next  tried  whether  with  carbon  electrodes,  in  a  good 
vacuum  of  either  hydrogen  or  nitrogen,  the  poles  of  the  arc 
were  of  equal  temperature,  as  Grove  had  said.  With  the 
vacuum  he  could  at  first  obtain,  the  positive  pole  was  the  hotter 
in  both  gases,  though  the  difference  of  temperature  was  less 
than  in  air.  He  then  tried  a  pressure  of  O'lmm.,  but  found 
that  as  soon  as  the  arc  was  struck  the  pressure  increased 
immensely,  owing  to  the  hot  vapour  sent  off  by  the  carbon 
poles.  He  continued  to  strike  the  arc  and  improve  the  vacuum 
till  at  last  the  pressure  hardly  increased  at  all  when  the  arc 
was  struck,  "at  the  same  time  the  difference  of  temperature 
between  the  carbons  disappeared"  It  was  thus  evident  that 
Grove  was  right,  and  that  Stenger  had  only  been  unsuccessful 
before  because  his  vacuum  was  not  good  enough.  On  account 
of  the  carbon  vapour  he  could  never  get  a  vacuum  of  less  than 
from  1mm.  to  2 mm.,  otherwise  he  thought  it  probable  that  he 
might  have  succeeded  in  making  the  negative  pole  hotter 
than  the  positive,  in  which  case  he  would  have  passed 
from  an  arc  to  a  tube  discharge  by  simply  improving  the 
vacuum. 

The  increase  of  pressure  when  the  arc  was  struck  was  in 
some  instances  very  striking,  and  was  evidently  of  the  same 
kind  as  that  obtained  by  De  la  Rue  and  Miiller.  Also  the 
moment  contact  was  broken,  the  pressure  fell  to  what  it  had 
been  before  contact  was  made,  as  it  had  done  in  their 
experiments. 


46  THE  ELECTRIC  ARC. 

Stenger  considered  that  the  small  resistance  of  the  gaseous 
part  of  the  arc  was  due  to  the  presence  of  metallic  vapour,  of 
which,  he  said,  there  was  a  considerable  amount,  even  when 
the  poles  were  of  carbon. 65 

Shortly  afterwards  Edlund  summed  up  the  results  obtained 
by  himself,  Frolich,  Peukert,  and  Von  Lang,  and  proceeded  to 
consider  Peukert's  view  that  the  term  a  in  the  equation 
r  =  a  +  b  I  represented  a  resistance  of  transition  at  the  surface 
of  contact  of  the  electrodes  and  the  arc.  Edlund  concluded 
that,  since  the  value  of  the  back  E.M.F.  of  the  arc — 39  volts 
— obtained  by  Von  Lang's  method,  which  depended  on  the 
measurement  of  the  true  resistance  of  the  arc,  did  not  differ 
much  from  either  the  values  obtained  by  himself,  41*97  volts, 
or  by  Frolich,  39  volts,  or  by  Peukert,  35  volts,  it  followed 
that  there  was  no  resistance  of  transition  in  the  voltaic  arc,  and 
that,  therefore,  the  entire  diminution  of  the  strength  of  the  current 
tvhich  resulted  from  the  production  of  the  arc-light  was  caused  by 
the  resistance  of  the  arc  bl  and  by  the  E.M.F.  contained  in  it.66 

In  1886  Messrs.  Cross  and  Shepard  made  experiments  with 
both  silent  and  hissing  arcs  to  determine  whether  the  apparent 
resistance  of  the  "  whistling"  arc  was  a  linear  function  of  the 
length  for  a  constant  current,  as  it  had  been  shown  to  be  by 
Edlund  and  others  for  a  silent  arc.  They  used  currents  varying 
from  3-27  to  10 -04  amperes,  and  lengths  of  arc  from  0  25/32  to 
16/32  of  an  inch,  and  found  that  for  a  given  current  the  resis- 
tance of  the  whistling  arc  could  be  represented  by  a  straight 
line  in  terms  of  the  current,  but  that  this  line  was  steeper  than 
that  representing  the  resistance  of  a  silent  arc  for  the  same 
current. 

Without  expressing  any  opinion  as  to  the  existence  of  an 
inverse  E.M.F.  in  the  arc,  they  gave  this  name,  for  convenience 
sake,  to  the  product  A  a,  where  A  was  the  current  and  a  was 
given  by  the  resistance  equation 

r  =  a  +  b  I, 

and  they  found  by  experiment  that  both  with  silent  and  with 
whistling  arcs  this  product  A  a  diminished  as  the  current 
increased,  having  a  mean  value  of  39 '33  volts  for  a  silent  and 
14'98  volts  for  a  whistling  arc.  With  very  long  arcs,  however, 
and  with  long  arcs  in  which  metallic  salts  were  volatilised, 


A  SHORT  HISTORY  OF  THE  ARC.  47 

they  found  that  the  apparent  resistance  tended  to  become 
abnormally  small. 

Next  they  experimented  with  an  inverted  arc,  and  although 
it  was  much  less  steady  than  the  upright  arc,  the  results 
obtained  were  practically  the  same. 

The  arc  having  been  restored  to  its  original  position,  they 
surrounded  the  positive  carbon  with  a  deep  cup-shaped  shield 
of  fire-clay  in  order  to  retain  the  heat,  and  found  that  this 
increased  the  inverse  E.M.F.  both  for  silent  and  for  whistling 
arcs,  and  that  it  also  increased  the  length  of  the  arc  at  which 
whistling  occurred  for  each  particular  current.  On  the  other 
hand,  b,  the  coefficient  of  I,  was  diminished. 

Cooling  the  positive  carbon  with  a  water  jacket  caused  the 
E.M.F.  to  fall  to  117  volts  for  a  current  of  7  amperes 
and  to  56  volts  for  one  of  8  amperes. 

Finally,  a  few  experiments  were  made  on  an  arc  in  a  partial 
vacuum  under  a  pressure  of  only  4in.  of  mercury.  The 
equation  r  =  a  +  bl  still  held,  but  the  arc  hissed  for  all  the 
lengths  and  currents  tried,  and  the  lines  connecting  resistance 
and  length  were  less  steep  than  those  for  hissing  arcs  under 
normal  pressure  for  the  same  currents  respectively.67 

In  the  same  year,  1886,  Nebel  used  a  method  somewhat 
similar  to  Von  Lang's  for  the  determination  of  the  back  E.M.F. 
of  the  arc,  but  instead  of  the  two  arcs  employed  by  Von  Lang 
his  method  required  but  one.  He  did  not  publish  the  results 
of  his  experiments,  but  contented  himself  with  making  a  mathe- 
matical determination  of  the  conditions  that  should  exist 
between  such  results  when  obtained. 

He  afterwards  made  experiments  for  the  purpose  of  deter- 
mining the  P.D.  that  existed  between  carbon  electrodes  when  arcs 
of  various  lengths  were  burning  with  various  currents  flowing. 
He  used  two  carbons  of  equal  diameter,  of  which  the  positive 
was  cored  and  the  negative  uncored.  Pairs  were  employed 
having  diameters  of  10,  12,  14  and  16  mm.  He  found  the 
depths  of  the  craters  by  filling  them  with  half-melted  sealing 
wax,  which  he  afterwards  measured  with  a  spherometer. 

Nebel  drew  curves,  the  first  of  the  kind  ever  published, 
connecting  the  P.D.  between  the  carbons  with  the  current 
flowing  for  various  constant  lengths  of  arc;  and  he  pointed  out 
that,  with  the  carbons  he  used  the  P.D.  diminished,  fell  to  a 


48 


THE  ELECTRIC  AEG. 


minimum,  and  then  rose  again  as  the  current  increased  from  ita 
lowest  to  its  highest  value.  The  minimum  P.D.,  as  he  remarked, 
corresponded  with  a  larger  current  the  longer  the  arc. 

Table  IV.-(Xebel). 

Positive  Carbon  Cored,  Negative  Uncored. 


10  mm.  Carbons. 

12  mm.  Carbons. 

Amperes. 

1  cm. 
1-8 

2  cm. 
3-1 

3  cm. 
4-4 

4  cm. 
5-6 

5  cm. 
6-9 

6  cm. 
8-2 

L  cm. 
2-1 

2cm. 

3-4 

3cm. 
4-7 

4cm. 
5-9 

5  cm. 
7-2 

6cm. 
8-5 

P,  D.  between  the  Carbons  in  Volts. 

P.  D.  between  Carbons  in  Volts. 

4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
28 

46-28 
43-18 
42-08 
43-00 
43-40 
43-46 
43-52 
43-72 
37-6* 

55-88 
49-32 
46-16 
45-06 
45-30 
46-03 
46-26 
46-58 
46-74 
46-78 
4700 
44-14* 

51-94 
50-20 
49-24 
48-38 
47-68 
47-02 
47-18 
47-32 
47-69 
47-90 

55-18 
51-82 
51-22 
50-84 
50-14 
49-66 
49-96 
49  '96 
50-66 
50-84 

57-26 
55-88 
54-64 
53-36 
51-06 
50-98 
5114 
51-38 
51-84 

57-06 
56-20 
56-02 
55-62 
54-76 
53-10 
53-92 

42-66 
40-90 
40-16 
40-82 

40-90 
41-82 
41-98 

49-00 
45-36 
44-12 
44-34 

44-52 
45-92 
4616 

51-68 

47-40 
47-32 
47-72 
47-82 

4814 

49-72 
49-98 

50-74 
50-54 
50-06 
49-42 

56-60 

50-06 
51-58 
51-80 

55-04 
54-10 
53-66 
53-23 
52-04 
52-10 
52-22 
52-62 
53-22 
53-22 

57-62 
56-44 
56-36 

56-08 
56-52 
57-10 

14  mm.  Carbons. 

16  mm.  Carbons. 

1  cm. 
2-7 

2cm. 
4-0 

3  cm. 
5-2 

4cm. 
6-7 

5cm. 
7-8 

— 

1  cm. 
2-7 

2cm. 
4-0 

3cm. 
5-2 

4  cm. 
6-5 

— 

— 

10 
12 
14 
16 
20 
24 
26 
28 
30 
32 
34 
35 
38 

40-84 
40-00 
39-80 
40-10 
40-34 
40-39 
40-78 
41-23 
37-68" 

44-42 
43-34 
42-46 
42-07 
42-16 
42-56 
42-80 
42-96 
43-40 

51-16 

48-80 
46-70 
45-78 
45-08 
45-32 
46-04 
46-50 
46-68 

55-50  58-66 
51-7653-56 
49-12'51-20 
48-6850-70 
48-42  50-54 
47-9250-76 
48-2250-78 
48-7850-82 
48-92  50-90 

40-76 

42-98 

48-80 

... 

... 

... 

... 

40-36 
40-30 
40-52 

42-44 
42-32 
42-08 

45-96 
45-74 
45-64 

55-46 
50-42 
48-88 

... 

... 

40-58 

41-94 

45-72 

47-44 

... 

... 

41-12 

42-12 

45-72 

47-20 
47-74 
47-90 
48-06 

... 

42-22 

45-78 

He  also  drew  curves  connecting  the  P.D.  between  the 
carbons  with  the  length  of  the  arc  for  constant  currents, 
but  did  not  publish  them.  These  curves  were  not  all  straight 


Hissing. 


A  SHORT  HISTORY  OF  THE  ARC.  49 

lines,  as  he  pointed  out,  but  dipped  down  towards  the  axis  of 
length  for  small  currents.  He  remarked  that  they  made  a 
smaller  angle  with  the  axis  of  length  the  larger  the  current, 
and  applied  Frolich's  formula 

V  =  a  +  bl 

to  them,  thus  treating  them  as  if  they  had  been  straight  lines. 
He  found  what  he  considered  to  be  the  values  of  a  and  b  in 
this  equation  for  each  of  his  sets  of  results,  and  from  these 
values  it  appeared  that  with  his  carbons  a  increased  as  the 
current  increased.  He  came  to  the  conclusion,  however,  that 
it  was  still  uncertain  whether  a  depended  upon  the  current  or 
not,  but  showed  that  it  diminished  as  the  diameter  of  the 
carbons  increased.  He  considered  his  experiments  to  prove 
that  b  depended  on  the  current. 

He  calculated  the  apparent  resistances  of  the  arc  from  the 
P.D.'s  and  currents  and  plotted  curves,  which  he  published, 
connecting  these  with  the  lengths  of  the  arc  for  various 
constant  currents. 

In  the  table  of  Nebel's  results  on  p,  48,  the  top  line  gives 
the  magnified  length  of  the  arc  as  seen  on  the  screen,  7'89 
times  its  true  length  ;  the  second  line  gives  this  length  with 
the  depth  of  the  crater  added.  Each  P.D.  is  the  mean  of  five 
observations.68 

Arons  tried  to  find  the  true  resistance  of  the  arc  by  placing 
it,  with  the  battery  producing  it,  in  one  arm  of  a  Wheatstone's 
bridge.  One  of  the  diagonals  of  the  bridge  contained  the 
stationary  coil  of  a  dynamometer,  while  the  other  contained 
the  secondary  coil  of  an  induction  apparatus.  The  three  arms 
of  the  bridge  were  adjusted  until  this  inductor  sent  no  current 
through  the  stationary  coil  of  the  dynamometer,  as  proved  by 
there  being  no  deflection  of  the  movable  coil  of  the  dynamo- 
meter, which  was  traversed  by  an  independent  alternating 
current  produced  by  an  auxiliary  induction  apparatus. 

Next  the  arc  was  short-circuited  and  a  resistance  put  in 
its  place  of  such  a  value  that,  without  making  any  alteration 
in  the  resistances  of  the  other  three  arms  of  the  bridge,  no 
current  was  sent  through  the  dynamometer-diagonal  of  the 
bridge  by  the  secondary  coil  of  the  first  inductor  which 
formed  the  other  diagonal.  Under  these  circumstances  he 
considered  that  this  added  resistance  was  equal  to  that  of  the 


V    ' 
60  THE  ELECTRIC  AUG. 

arc.  With  a  current  of  3'4  amperes,  Arons  found  this  resistance 
to  be  2*1  ohms,  and  the  back  E.M.F.  40*6  volts,  while  with  a 
current  of  4*1  amperes  he  found  the  resistance  to  be  1PG  ohms, 
and  the  back  E.M.F.  39-6  volts.  The  length  of  the  arc  is 
not  stated  in  his  Paper.69 

In  the  same  year  Von  Lang  repeated  his  method,  illustrated 
in  Fig.  TSi,  and  now  found  37  volts  as  the  value  of  the  back 
{  E.M.F.  between  the  carbons.  This  method  he  also  employed  with 
electrodes  of  other  materials,  and  he  found  that  when  they  were 
both  composed  of  one  of  the  following  substances,  arranged  in 
the  order  indicated  —  platinum,  nickel,  iron,  copper,  zinc,  silver, 
cadmium  —  the  back  E.M.F.  of  the  arc  fell  steadily  from  about 
27  volts  for  the  platinum  electrodes  to  about  10  for  those 
of  cadmium. 

Von  Lang  expressed  V,  the  P.D.  between  the  carbons,  as 


but  a,  the  back  E.M.F.,  was,  for  no  one  of  the  pairs  of  electrodes 
used,  given  with  a  probable  error  of  less  than  +  or  -  3  per 
cent.,  and  in  some  cases  it  was  as  high  as  +  or  -  34  per  cent.70 
Uppenborn,  in  1888,  found  from  experiments  with  a  constant 
current  of  7  '7  amperes,  producing  an  arc  with  10mm.  carbons, 
that  « 


where  I  was  the  length  of  the  arc.  a,  however,  in  this  equation 
varied  from  35'4  to  45'4,  and  b  from  1-74  to  3-2. 

When  the  current  was  increased  he  found  that  a  increased, 
while  b  diminished,  a,  he  considered  might  be  replaced  by 
x  +  y  A,  where  A  was  the  current  and  x  and  y  depended  on  the 
carbons.  He  concluded  that,  since  a  increased  both  with  increase 
of  current  and  with  increase  in  the  cross  section  of  the  arc,  the 
effects  were  probably  due  to  surface  resistance  rather  than  to  a 
back  E.M.F.73 

Dr.  Feussner,  in  the  same  year,  pointed  out  that  by  the 
method  used  by  V.  Lang,  Arons  and  others,  only  part  of  the 
resistance  of  the  arc  was  measured.  The  method  depended,  he 
considered,  upon  Ohm's  law  and  Kirchhoff's  two  laws,  for 
which  it  was  essential  that  both  the  E.M.F.  and  the  resistance 
should  be  independent  of  the  current  flowing.  In  the  arc,  the 


A  SHORT  HISTORY  OF  THE  ARC.  51 

second  of  these  conditions  was  not  fulfilled,  for  the  conductivity 
of  the  arc,  and  hence  its  resistance,  depended  on  the  current 
flowing. 

His  idea  was  that  the  resistance  of  the  arc  should  be  obtained 
•simply  by  dividing  the  P.D.  between  the  carbons  by  the  current, 
and  hence  that  it  could  be  measured  by  the  Wheatstone's 
bridge  used  in  the  ordinary  way.  He  considered  that  there 
was  no  direct  proof  of  the  non-existence  of  a  -back  EJiOVrn^ 
tnoare/'but  as  it  apparently  existed  in  alternate  current  as  well 
.as  in  direct  current  arcs,  it  could  not  be  a  thermo-electric  effect, 
since  the  temperature  of  the  electrodes  must  be  very  nearly 
equal  in  alternate  current  arcs. 

He  pointed  out  that  gases,  even  afc  a  high  temperature,  are 
non-conductors,  and  that  therefore  the  arc  itself  cannot  consist 
of  gases,  but  must  be  volatilised  carbon.  He  considered,  there- 
fore, that  in  order  that  an  arc  should  exist,  at  least  one  of  the 
electrodes  must  be  at  its  temperature  of  volatilisation.  This 
temperature,  he  said,  if  there  were  no  other  source  of  heat  than 
the  current,  could  only  be  given  by  the  current,  i.e.  the  current 
•must  "encounter  a  transition  resistance  so  great  that  the 
consequent  loss  of  P.D.  multiplied  by  the  current  strength 
must  be  equivalent  to  the  energy  given  out  at  the  place  in 
question,  either  as  heat  or  light,  at  the  temperature  of  the 
beginning  of  volatilisation.  Hence  the  transition  resistance 
must  be  the  greater  the  higher  the  temperature  of  volatilisa- 
tion." 

Dr.  Feussner  gave  reasons  for  considering  that  the  full 
equation  representing  the  relations  between  the  P.D.,  current, 
and  length  of  the  arc  should  be 


where  E  is  the  back  E.M.F.  of  the  arc, 
J    is  the  current  flowing, 
Ji  is  the  unit  of  current, 
W  is  the  total  true  resistance  of  the  arc, 
WQ  is  that  part  of  the  resistance  of  the  arc  that  is 

independent  of  the  current  flowing, 
wl  is  the  part  of  the  resistance  that  depends  on  the 

current  when  unit  current  is  flowing. 

v.9. 


62  THE  ELECTRIC  ARC. 

He  finally  gave  the  three  qualities  necessary  in  electrodes  for 
the  arc  between  them  to  give  the  most  light  with  the  least 
power  expended.  They  were 

(1)  High  temperature  of  volatilisation. 

(2)  Great  power  of  radiation. 

(3)  Small  heat  conductivity.74 

Fig.  17  shows  the  apparatus  used  by  Lecher  to  try  to  find  a 
back  E.M.F.  in  the  arc  between  carbon  electrodes. 

D  was  the  gramme  dynamo,  from  which  the  conductor  a  led 
to  the  arc  L,  and  thence  through  a'  through  a  commutator  c  c 
to  the  galvanometer  G.  From  the  other  terminal  of  G  the 
conductor  went  through  cc  again  and  through  V  and  b  back 
to  the  machine.  The  galvanometer  had  a  stop  so  that  the 
needle  could  only  move  in  one  direction,  and  as  the  full 
current  from  the  dynamo  would  have  carried  the  needle  far 
beyond  the  scale,  a  shunt  d  was  inserted  in  the  galvanometer 
circuit.  The  commutator  c  c  was  first  arranged  so  that  when. 


FIG.  17. 

the  arc  was  burning  the  needle  was  deflected.  Next  the 
commutator  was  reversed,  so  that,  but  for  the  galvanometer 
stop,  the  needle  would  have  given  the  same  deflection  as 
before,  only  in  the  opposite  direction.  The  shunt  d  was  then, 
cut  out,  so  that  had  the  needle  been  free  to  move  the  deflection- 
would  have  been  from  five  to  seven  times  as  great  as  the  whole 
length  of  the  scale.  The  machine  was  now  short  circuited  at 
a  b  for  a  very  short  time,  and  would  therefore  not  act  over  the 
remainder  of  the  circuit,  which  might  thus  be  considered  as  a 
closed  circuit.  Lecher  considered  that  if  there  were  a  back 
E.M  F.  in  the  arc,  the  back  current  created  by  it  should  now 
have  caused  a  deflection  of  the  needle  of  the  galvanometer, 
which  was  free  to  move  in  the  direction  caused  by  such  a 
current.  No  such  deflection  was  observed,  but  as  both  stop 
and  galvanometer  needle  were  a  little  springy  a  slight  deflec- 
tion followed  on  the  short  circuiting,  such  as  might  have 


A  SHORT  HISTORY  OF  THE  ARC.  53 

been  caused  by  a  back  E.M.F.  of  2  volta  or  so.  That  this 
deflection  was  really  caused  by  spring  and  not  by  a  back 
E.M.F.  was  shown  by  the  fact  that  the  deflection  of  the  needle 
was  the  same,  whether  the  dynamo  was  short-circuited  at  a  b 
or  at  a  b'. 

Lecher  measured  the  P.D.  between  the  carbons  when  the 
arc  was  burning  under  various  conditions  by  means  of  a  Thom- 
son electrometer.  The  carbons  were  5mm.  in  diameter,  the 
current  about  5  amperes,  and  the  length  of  arc  2mm.  The 
following  table  gives  the  various  conditions  and  positions  of 
the  carbons  and  the  results  of  the  experiments  : — 

Table  V. — (Lecher.) 


State  of  Carbons. 


P.D.  between 
Position  of  Carbons.  Carbons 

in  Volts. 


Horizontal    |  42 

52 
48 


Ordinary    

Negative,  heated  by  gas  burner 

Positive         „  „ 

Both  cooled  by  being  wound"} 

with  thick  copper  wire  up  >  I          „  

to  points J  j 

Ordinary    Vertical,positive  carbon  above 


„       negative 
Lower  cooled  to  tip  by  mer- )  „       positive 

cury  bath  in  water  jacket  J  „       negative 


less  than  35 

47 
46 
43 
41 


The  carbons  enveloped  in  mercury  developed  mushrooms,  and 
the  arc  was  very  unsteady  during  the  last  experiment.  Lecher 
•considered  the  results  to  prove  that  the  P.D.  between  the 
sarbons  depended  on  their  temperatures.  He  thought  hissing 
was  caused  by  the  discharge  springing  to  and  fro  to  cooler 
places  as  the  previous  places  became  too  hot,  and  thus  setting 
up  a  vibration  which  produced  sound. 

Lecher  used  an  exploring  carbon  of  l'2mm.  diameter  to  find 
the  P.D.  between  each  of  the  carbons  and  the  arc.  By  placing 
the  exploring  carbon  vertically  midway  between  the  carbons 
of  a  horizontal  arc,  he  obtained  35  volts  as  the  P.D.  between 
the  positive  carbon  and  the  exploring  carbon,  and  10  volts 
as  the  P.D.  between  the  exploring  carbon  and  the  negative. 
He  found  that  the  exploring  carbon  could  be  some  little 
distance  out  of  the  visible  arc  without  the  P.D.  between 
it  and  either  of  the  other  carbons  being  materially  altered. 


54  THE  ELECTRIC  ARC. 

Using  a  Ruhmkorff  coil  and  a  condenser,  he  found  that  the* 
silent  arc  was  not  discontinuous,  but  that  the  hissing  arc  was.7s 

Uppenborn  also  explored  the  arc  with  a  carbon  rod,  having 
tried  copper  and  platinum  wires  embedded  in  clay,  steatite, 
and  glass  tubes,  to  no  purpose.  He  found  that  with  arcs 
of  from  6mm.  to  16mm.  in  length,  the  P.D.  between  the 
positive  carbon  and  the  exploring  carbon  placed  near  it,  varied 
from  38  volts  to  32'5  volts,  while  he  found  only  5  volts  P.D. 
between  the  negative  carbon  and  the  exploring  carbon  placed 
near  it.  He  gave  a  very  good  description  of  the  shape  of  the 
arc.76 

Luggin,  in  a  long  and  very  interesting  paper,  discussed  the 
Wheatstone's  bridge  methods  previously  used  for  measuring 
the  resistance  of  the  arc,  all  of  which  he  considered  were  open 
to  criticism.  He  pointed  out  that,  whereas  when  a  small 
increase  of  E.M.F.  was  applied  to  an  ordinary  conductor 
through  which  a  current  was  flowing,  the  P.D.  at  its  ends 
increased,  and  therefore  the  variation  of  P.D.  had  a  positive 
sign  ;  in  the  arc,  on  the  contrary,  an  increase  of  current  was 
attended  by  a  diminution  of  the  P.D.  between  the  ends  of  the 
carbons,  and  consequently  the  variation  of  the  P.D.,  caused  by 
an  increase  of  the  E.M.F.,  must  have  a  negative  sign. 

Having  shown  the  connection  between  the  resistances  in  an 
ordinary  Wheatstone's  bridge,  and  having  mentioned  that  the 
relation  remained  the  same  even  if  there  were  constant 
E.M.F.'s  in  all  the  arms,  he  continued  thus  :  "  If  now  an  arc 
were  started  in  the  arm  a,  while  in  all  the  other  resistances  the 
bridge  remained  unaltered,  then  the  P.D.  at  the  ends  of  a 
would  be  less  than  before,  and  we  should  have  to  conclude 
from  the  diminished  P.D.  that  the  resistance  w^  had  become 
less,  and  that  the  arc  had  a  negative  resistance." 

Luggin  himself  used  a  method  somewhat  similar  to  Von 
Lang's  for  finding  the  resistance  of  the  arc.  In  one  of  the 
arms  of  a  Wheatstone's  bridge  he  placed  an  arc,  in  the  second 
a  comparing  resistance  of  2  ohms,  and  in  the  third  and  fourth 
liquid  resistances  amounting  together  to  300  ohms.  In  one 
of  the  diagonals  was  a  battery  of  accumulators  and  a  rheostat 
to  regulate  the  current,  which  was  shunted  by  a  liquid  resis- 
tance of  600  ohms  and  an  electrically-driven  tuning-fork.  In 
the  second  diagonal,  a  condenser  and  telephone  were  in  series, 


A  SHORT  HISTORY  OF  THE  ARC 


65 


the  former  being  used  to  protect  the  telephone  from  the  direct 
current,  and  to  take  such  a  quantity  of  electricity  from  the 
alternating  current  as  to  allow  the  telephone  to  be  sufficiently 
sensitive. 

Luggin  attributed  the  fall  of  P.D.  between  the  carbons  that 
took  place  when  the  current  was  increased  to  a  diminution  in 
the  resistance  of  the  gaseous  medium  caused  by  its  rise  of 
temperature.  He  pointed  out  that  this  change  could  not  be 
an  instantaneous  one,  and  that  therefore  if  the  current  were 
alternated  with  sufficient  rapidity  the  P.D.  would  rise  and 
fall  with  the  current,  "  and  the  arc  would  show  a  positive 
resistance."  He  considered  that  the  reason  that  Arons  found 
a  positive  resistance  in  the  arc  was  that  the  alternating  current 
he  impressed  on  the  direct  current  in  his  arc  alternated  very 
rapidly,  and  he  was  quite  unable  to  understand  why  Frolich 
did  not  find  a  negative  resistance. 

To  find  the  variation  in  the  P.D.  between  the  carbons  when 
the  length  of  the  arc  was  varied  and  the  current  kept  constant, 
Luggin  used  two  Siemens  carbons  10mm.  in  diameter,  the 
positive  cored  and  the  negative  uncored.  For  each  figure  he 
took  the  mean  of  three  or  four  sets  of  observations.  The  fol- 
lowing table  gives  the  results  of  his  experiments  with  a  current 
of  7  amperes.  The  length  of  the  arc  is  given  in  scale  divi- 
sions, each  of  which  was  O434mm.  He  found  that  the  formula 

V  =  40-04  +  l-774  I, 

where  V  was  the  P.D.  between  the  carbons  in  volts  and  I  the 
length  of  the  arc  in  scale  divisions,  fitted  his  observations 
extremely  well,  as  will  be  seen  from  the  following  table. 

Table  VI. — (Luggin.}     Current  7  amperes. 
Positive  Carbon  Cored,  Negative  Uncored. 


L 

V  (volts)  observed. 

V  (volts)  calculated. 

Difference. 

i 

41-6 

41-81 

-0-21 

2 

43-3 

43-59 

-0-29 

3 

45-4 

45-36 

+  0-04 

4 

47-6 

47-14 

+  0-46 

5 

49-3 

48-91 

+  0-39 

6 

50-8 

50-68 

+  0-12 

7 

52-3 

52-46 

-0-16 

8 

53-9 

54-23 

-0-33 

56 


THE  ELECTRIC  ARC. 


Luggin  tried  using  a  horizontal  disc  of  carbon  15cm.  in  dia- 
meter as  one  of  the  electrodes  of  an  upright  arc,  and  a  carbon 
rod  for  the  other.  When  the  disc  was  placed  under  the  rod 
and  used  as  the  negative  electrode,  it  was  found  that  even  a 
very  slow  rotation  of  the  disc  extinguished  the  arc,  however 
strong  the  current.  When,  however,  the  disc  was  placed  above 
the  rod  and  used  as  the  positive  electrode,  it  could  be  rotated 
fairly  quickly  even  with  a  current  of  only  7  amperes,  and  with 
currents  of  from  27  to  33  amperes  it  could  be  rotated  very  fast 
indeed  without  the  arc  becoming  extinguished.  With  slow 
rotations  the  disc  was  pitted  with  small  craters,  but  with  the 
faster  ones  these  craters  ran  into  one  another.  When  the  arc 
hissed,  while  the  disc  was  still,  the  P.O.  between  the  carbons 
sank  as  usual  10  or  11  volts,  but  if,  while  the  hissing  continued 
the  disc  was  set  in  rotation,  the  P.D.  sank  from  3  to  5  volts 
lower  still. 

He  next  experimented  with  iron  electrodes,  and  finally  he  used 
an  exploring  carbon  to  find  the  difference  in  volts  between  the 
fall  of  potential  between  the  positive  carbon  and  any  point  in 
the  arc,  and  the  fall  of  potential  between  that  same  point  and 
the  negative  carbon.  This  difference  is  denoted  by  E  in  the 
following  table,  while  V  denotes  the  P.D.  between  the  carbons 
in  volts,  and  I  the  length  of  the  arc  in  mm.  Siemens  carbons 
were  used,  and  a  current  of  6 '8  amperes  for  the  first  set  of 
results,  and  one  of  849  amperes  for  the  second. 

Results  (I.)  were  obtained  with  ordinary  Siemens  carbons. 
Results  (II.)  with  carbons  sprinkled  with  soda. 

Table  VII.— (Luggin.) 


(I.) 


(II.) 


V 

E                        V 

E 

I 

39-8 

25-9 

17-9 

0-43 

2-9 

42-5 

27-1 

19-4 

1-76 

3-0 

46-3 

26'9 

20-0 

0-69 

3-9 

48-7 

32-2 

21-4 

3-77 

4-0 

49-3 

31-0 

22-6 

2-89 

5-0 

51-7 

33-3 

28-0 

7-00 

6-8 

52-7 

32-9 

57-7 

34-6 

From  the  immense  diminution  in  E  in  (II.),  caused  by  sprink- 
ling the  carbons  with  soda,  so  much  greater  than  the  corres- 


A  SHOUT  HISTORY  OF  THE  ARC.  57 

ponding  diminution  in  V,  Luggin  concluded  that  there  was  an 
enormous  leap  of  potential  at  the  positive  pole,  which  was 
almost  neutralised  by  sprinking  the  carbons  with  soda.  This 
onesidedness  diminished  as  the  length  of  the  arc  diminished, 
and  he  mentioned  that  once,  with  the  ordinary  Siemens 
carbons,  when  the  point  of  the  negative  carbon  was  entirely 
surrounded  by  the  crater,  V  was  35 '5  volts  and  E  was  as  low 
as  18-8  volts.77 

Dabs,  in  1888,  found  that  if  two  carbon  plates  were  placed 
one  above  the  other  with  a  distance  of  1mm.  between  them, 
and  a  blowpipe  flame  was  directed  on  to  the  lower,  so  as  to  carry 
carbon  particles  to  the  upper,  a  galvanometer  connected  with 
the  plates  showed  a  weak  current  flowing  against  the  blast. 
Also  that  if  a  carbon  plate  were  heated  on  an  oxyhydrogen 
flame  and  laid  on  a  cold  carbon  plate,  a  current  flowed  from 
the  cold  to  the  hot  plate.  With  copper  plates  the  effect  was 
less,  and  was  nil  with  iron.  Dubs  regarded  the  effect  as 
analogous  with  the  back  E.M.F.  in  the  arc,  and  considered 
that  that  depended,  at  any  rate  in  part,  on  the  mechanical 
action  of  the  current.79 

In  1889,  Luggin  followed  up  his  previous  researches  by  a 
long  and  close  investigation  of  the  arc  with  exploring  carbons. 
Some  parts  of  the  Paper  in  which  he  gave  the  results  of  these 
investigations  it  is  impossible  to  follow ;  for  not  only  is  the 
German  very  involved,  but  there  is  a  complete  dearth  of 
Figures,  and  the  explanations  given  are  too  scanty  to  enable 
the  reader  to  construct  these  for  himself.  This  is  all  the 
greater  pity,  as  Luggin's  work,  where  it  can  be  understood,  is 
both  original  and  suggestive. 

The  first  experiments  were  undertaken  to  find  out  how  the 
potential  varied  in  different  parts  of  the  same  cross-section 
of  an  arc  8mm.  in  length.  Siemens  carbons,  12mm.  in 
diameter,  were  used  for  the  electrodes,  and  Carre  carbons,  1mm. 
to  2mm.  in  diameter,  for  exploring.  These  always  burnt  to  a 
point  in  the  arc.  The  results  differed  according  as  the  positive 
carbon  was  solid  or  cored.  When  it  was  solid,  it  was  found 
that  when  one  exploring  carbon  just  touched  the  purple  core 
of  the  arc  and  another  just  dipped  into  the  outer  flame,  both 
in  the  lowest  cross-section  of  the  arc,  the  potential  of  the 
inner  carbon  was  three  volts  lower  than  that  of  the  outer  one. 


58  THE  ELECTRIC  ARC. 

For  higher  cross-sections  of  the  arc  the  case  was  reversed,  the 
inner  carbon  having  a  potential  two  volts  higher  than  the  outer 
in  the  cross-section  midway  between  the  electrodes.  When  the 
point  of  one  carbon  was  placed  at  the  centre  of  the  purple  core, 
and  that  of  the  other  touched  the  outer  flame  in  the  same 
cross-section,  the  potential  of  the  inner  carbon  was  higher  than 
that  of  the  outer.  When  the  positive  carbon  was  cored,  very 
little  difference  was  found  between  the  potentials  of  the  inner 
and  outer  portions  of  the  same  cross-section  of  the  arc,  which 
led  Luggin  to  doubt  if  the  differences  found  with  solid  carbons 
had  not  been  caused  by  the  exploring  carbon  itself. 

Luggin  found  that  a  thick  exploring  carbon  disturbed  the 
arc  considerably,  and  that  it  seemed  to  repel  it.  Its  insertion 
also  raised  the  P.D.  between  the  carbons,  and  sometimes  made 
the  arc  hiss  and  sing.  Putting  a  thick  exploring  carbon  about 
2mm.  from  the  positive  electrode  caused  two  arcs  to  form,  one 
between  the  positive  and  the  exploring  carbon,  and  the  other 
between  the  exploring  carbon  and  the  negative. 

An  exploring  carbon  of  l'3mm.  diameter  was  placed  with 
its  point  immediately  under  the  crater  (carbons  both  solid, 
12mm.  in  diameter),  with  a  current  of  15*5  amperes  flowing. 
The  P.D.  between  the  positive  and  exploring  carbons  was 
found,  from  five  measurements,  to  be  33 -7  ±  Of46  volts.  Chang- 
ing the  length  of  the  arc  appeared  to  have  no  influence  on  this 
P.D.  The  exploring  carbon  was  next  placed  in  the  arc,  with 
its  point  as  near  as  possible  to  the  bright  spot  on  the  negative 
carbon,  and  the  P.D.  between  exploring  and  negative  carbons 
was  found,  from  six  measurements,  to  be  8-78+  0*17  volts. 

This  one-sidedness  in  the  potential  of  the  arc,  which  Luggin 
called  E,  was  also  measured  in  another  way,  on  the  supposition 
that  the  fall  of  potential  in  the  arc  itself  was  perfectly  uniform. 
E  is,  of  course,  the  difference  between  the  fall  of  potential 
between  the  positive  electrode  and  the  exploring  carbon  and 
the  fall  of  potential  between  the  exploring  carbon  and  the 
negative  electrode.  If,  then,  the  exploring  carbon  is  placed  in 
the  middle  section  of  the  arc  and  v,  the  P.D.  between  the 
positive  and  exploring  carbons,  is  measured  simultaneously 
with  V,  the  P.D.  between  the  two  electrodes,  then 


A  SHORT  HISTORY  OF  THE  ARC.  59 

If  the  potential  of  the  exploring  carbon  differs  by  an  amount 
dv  from  the  surrounding  gases,  the  above  value  of  E  is  incor- 
rect by  2dv,  as  Luggin  showed.  He  made  measurements  of 
V  and  v  in  the  manner  described,  only  allowing  the  exploring 
carbon  to  touch  the  outer  edge  of  the  flame  surrounding  the 
arc,  however,  so  as  to  cause  the  least  possible  disturbance  to 
the  arc.  This  probably  introduced  some  error,  but  the  value 
of  E  thus  obtained  was  the  same  as  with  the  earlier  experi- 
ments, namely,  24*9  volts.  Other  measurements  made  with  a 
current  of  16\S  amperes  and  with  increasing  length  of  arc  gave 
V  =  49  -9  volts.  E  =  24-5  volts. 

V  =  53'8     „  E  =  25-8     „ 

V  =  65-2      „  E  =  25-6     „ 

With  cored  positive  and  solid  negative  carbons  12mm.  in  dia- 
meter the  following  values  were  obtained  with  increasing  length 
of  arc  : — 

V  =  44-9  volts.  E  =  28-3  ±  0-24 

V  =  51-4     „  E  =  29-6±0-61 

V  =  55-2     „  E  =  30-3  ±0-29 

V  =  58-7     „  E  =  31-4±0-40 

Y  =  64-8     „  E  =  34-4±0'54 

For  these  last  experiments  the  exploring  carbon  was  placed  by 
eye  only.  Luggin  pointed  out  that  the  two  sets  of  experi- 
ments show  that  while  with  solid  carbons  the  P.D.s  between 
the  positive  carbon  and  the  middle  cross-section  of  the  arc  and 
between  the  same  cross-section  and  the  negative  carbon 
increase  at  about  the  same  rate  with  increasing  length  of  arc, 
with  a  cored  positive  carbon  the  P.D.  between  the  positive  and 
the  middle  cross-section  increases  more  rapidly  than  the  P  D. 
between  that  cross-section  and  the  negative  carbon. 

From  another  experiment  it  appears  that,  at  least  with  a 
cored  positive  carbon,  the  potential  of  the  arc  itself  does  not 
fall  at  a  perfectly  uniform  rate,  as  was  supposed  in  making  the 
experiment.  He  fastened  two  carbons,  one  on  either  side  of  a 
plank  3mm.  thick,  so  that  they  were  held  at  a  constant  vertical 
distance  from  one  another.  He  then  placed  the  carbons  horizon- 
tally, so  that  the  point  of  the  upper  was  vertically  over  that  of 
the  under,  in  an  arc  burning  between  positive  cored  and  solid 
negative  carbons.  According  as  the  pair  of  carbons  was  near 
the  positive  or  negative  electrode,  the  P.D.  between  them  was 


60  THE  ELECTRIC  ARC. 

12*4  or  8-05  volts.     The  same  experiment  was  not  tried  with 
two  solid  electrodes. 

Placing  an  exploring  carbon  in  the  outside  aureole  of  the  arc, 
near  the  positive  carbon,  the  P.D.  between  the  positive  and 
exploring  carbons  was  found  to  be  about  1  volt  greater  than 
when  the  latter  was  placed  as  near  as  possible  to  the  centre  of 
the  crater.  Luggin  considered  these  experiments  showed  that 
the  P.D.  between  the  positive  carbon  and  the  surrounding  gases 
was  constant  as  a  first  approximation. 

He  gave  a  careful  description  of  the  different  parts  of  the  arc 
and  carbons,  and  mentioned  that  the  outer  green  part,  or 
aureole,  as  he  called  it,  started  higher  up  the  positive  carbon  than 
the  edge  of  the  crater,  and  that  there  was  a  space  between  it 
and  that  carbon  wide  enough  for  him  to  insert  a  thin  slip  of  car- 
bon into  it.  He  mentioned  that  carbon  pencils  glowed  brightly 
directly  they  were  placed  within  the  aureole,  and  that  the  latter 
widened  out  where  it  touched  these  pencils.  He  also  noticed 
that  the  arc  proper  and  the  aureole  varied  in  form  according  to 
the  material,  cross-section  and  position  of  the  electrodes.  He 
described  an  upright  arc  between  solid  carbons  as  being  like  an 
inverted  bell  standing  on  the  point  of  the  negative  carbon,  and 
said  that  with  long  arcs  the  middle  cross-section  of  the  arc  gave 
less  light  than  the  ends,  and  that  this  was  particularly  the  case 
with  cored  carbons,  or  with  carbons  in  which  volatile  salts  were 
mixed.  He  suggested  also  that  the  appearance  of  dividing 
itself  into  two  unequal  parts,  which  he  observed  in  the  arc  with 
cored  carbons,  was  connected  with  the  irregularity  in  the  fall 
of  potential  near  the  positive  and  negative  electrodes  that  he 
had  found  to  exist. 

Some  experiments  with  hissing  arcs  between  solid  carbons 
led  Luggin  to  observe  that  the  hissing  took  place  when  the 
current  was  so  strong  that  the  crater  filled  the  whole  of  the  end 
of  the  positive  carbon.  This  is  a  very  important  point  that  he 
was  the  first  to  observe.  He  noticed  also  that  the  longer  the  arc 
the  larger  the  current  that  could  be  used  before  the  arc  hissed  ; 
but  that  with  longer  arcs  the  end  of  the  carbon,  and  therefore  the 
crater,  was  larger.  With  long  silent  arcs  he  found  that  the  end  of 
the  positive  carbon  was  convex,  instead  of  its  having  a  crater. 

In  the  following  table  he  called  the  ratio  of  the  current 
strength  to  the  size  of  the  surface  of  the  end  of  the  positive 


A  SHORT  HISTORY  OF  THE  ARC.  61' 

carbon,  D ;  hence,  when  the  current  is  measured  in  amperes 
and  the  surface  of  the  carbon  in  millimetres,  D  is  the  current 
strength  in  amperes  per  millimetre  of  end  of  carbon. 

Table  VIU.—(Luggin.) 


I  (mm.}. 

A  (Amperes). 

Diameter  of  End- 
surface  (sq.  mm.) 

D  (Ampere). 

3-7 
8-5 

19-2 
26-3 

6-87 
8-25 

0-51 
0-49 

Luggin  found  that  the  quantity  he  called  E,  i.e.  the  difference 
between  the  fall  of  potential  between  the  positive  carbon  and 
the  arc,  and  the  fall  of  potential  between  the  arc  and  the  negative 
carbon,  was  somewhat  smaller  with  hissing  than  with  silent 
arcs,  showing  that  the  fall  of  potential  that  took  place  when 
the  arc  began  to  hiss  was  chiefly  between  the  positive  carbon 
and  the  arc. 

He  tried  to  find  evidences  of  polarisation  and  hence  a  back 
E.M.F.  in  the  arc  immediately  after  the  current  was  cut  off, 
but  was  unsuccessful,  and  he  considered  that  his  experiments 
showed  that  there  is  no  important  back  E.M.F.  in  the  arc 
O005  second  after  the  current  is  turned  off.80 

In  1890  Prof.  Ayrton,  with  some  of  his  students  at  the 
Central  Technical  College,  began  the  series  of  experiments 
that  were  described  in  the  Paper  he  read  at  the  Electrical 
Congress  in  Chicago  in  1893.  The  Paper  was  unfortunately 
burnt  before  it  could  be  published,  but  the  experiments  and 
their  results,  of  which  the  laboratory  notes  were  retained,  will 
be  discussed  later  on. 

In  1891,  in  an  account  that  included  a  revision  of  all  that 
was  known  of  the  physics  of  the  arc  up  to  date,  Prof.  Elihu 
Thomson  mentioned  that  he  had  found  that,  while  both  short 
and  long  arcs  could  be  made  to  burn  steadily,  there  was  an 
intermediate  stage  of  flickering  and  unsteadiness. 

He  considered  that  the  hollowness  of  the  crater  was  due 
to  the  evaporation  of  carbon  from  its  surface,  and  that  the 
temperature  of  the  crater  was  that  of  the  boiling-point  of 
carbon,  or,  "  more  correctly,  of  sublimation  at  atmospheric 
pressure."  He  found  that  the  carbon  of  the  crater  was  in  a 
plastic  state,  and  proved  it  by  pressing  the  carbons  together 


. 
•62 


THE  ELECTRIC  ARC. 


with  arcs  of  from  150  to  200  amperes,  and  finding  that  they 
would  fit  each  other  perfectly  afterwards.  He  was  also  able  to 
bend  sticks  of  carbon  a  quarter  of  an  inch  thick,  by  passing  a 
big  enough  current  through  them  almost  to  vaporise  them, 
and  causing  them  to  emit  a  light  nearly  as  intense  as  that  of 
the  arc.  Hence  he  argued  that  it  was  probable  that  carbon 
might  be  liquefied  if  subjected  to  the  temperature  of  the  arc 
under  high  pressure  in  an  inert  gas. 

He  considered  that  the  formation  and  maintenance  of  the 
arc  might  be  due  to  electrolytic  action,  the  hot  vapour  taking 
the  part  of  the  bath,  and  acting  by  a  molecular  interchange  of 
carbon  atoms.  He  mentioned  that  constant  potential  arcs 


65 


CO 


.?  55 


50 


45 


40 


35 


A 4. 


r 


Q 


0  6  10  15  20  25  30  35  40 

Current  in  Amperes. 

FIG.  18. 

were  impossible,  and  that  "  for  stability  the  resistance  should 
not  be  dependent  wholly  on  the  current  passing."81 

series  of  articles  on  the  alternate-current  arc,  published 
),  M.  Blondel  showed  how,  with  a  direct-current  arc,  to 
determine  graphically  the  conditions  of  dynamo  and  of  resist- 
ance outside  the  arc,  so  that  a  steady  arc  of  given  length 
might  be  maintained  between  carbons  of  given  diameter. 

Having  drawn  experimentally  the  curve  MNP  (Fig.   18), 
which   showed    the    connection    between    the    P.D.   at    the 


A  SHOUT  HISTORY  OF  THE  ARC.  03 

terminals  of  the  lamp  and  the  current  flowing  while  the  arc 
was  maintained  at  the  given  constant  length,  he  drew  QQ, 
the  characteristic  of  the  circuit  taken  at  the  terminals  of  the 
lamp.  He  then  pointed  out  that  if  this  curve  cut  M  N  P  at  N, 
the  necessary  and  sufficient  condition  for  stable  equilibrium 
was  that  Q  Q  should  cut  M  P  from  above  downwards  in  the 
direction  of  increase  of  current.  If  the  potential  of  the 
dynamo  were  a  constant  V,  represented  by  the  horizontal 
straight  line  A  C,  a  resistance  R  would  have  to  be  added 
to  the  lamps,  such  that  the  new  characteristic  of  the  feeding 
circuit  A  B  (E  =  V  -  R  A)  should  satisfy  the  preceding  condition. 

Suppose,  for  instance,  that  MNP  were  the  curve  for  an  arc 
of  4mm.,  and  that  E  D,  the  tangent  to  M  N  P  at  N,  cut  the 
axis  of  volts  at  the  height  of  55  volts.  Then,  as  M.  Blondel 
pointed  out,  it  is  impossible  to  supply  an  arc  of  4mm.  with 
a  current  of  25  amperes  with  a  constant  potential  of  less  than 
55  volts,  with  the  given  carbons.  And  in  order  that  the  arc 
should  be  perfectly  steady,  the  constant  potential  of  the 
dynamo  would  have  to  be  60,  or  even  65  volts.82 

Cravath  made  many  experiments  in  1892  to  discover  the 
causes  of  hissing  in  the  arc.  He  considered  that  the  principal 
of  these  were  air  currents,  impurities  in  the  carbons,  and  short- 
ness of  the  arc.  As  he  noticed  that  during  hissing  the  stream 
of  carbon  vapour  appeared  to  issue  from  a  part  only  of  the 
crater,  and  that  this  part  was  constantly  changing,  it  occurred 
to  him  that  perhaps  hissing  was  due  to  the  heating  and  cooling 
of  the  carbons  caused  by  this  change  of  position.  He,  there- 
fore, tried  the  effect  of  moving  one  carbon  horizontally  over  the 
other  while  a  steady  silent  arc  \vas  burning.  When  the  positive 
carbon  was  pointed  and  the  negative  flat  the  arc  burned  silently 
as  before,  but  when  the  negative  carbon  was  pointed  and  the 
positive  flat,  each  change  of  position  caused  a  hiss. 

Cravath  measured  the  diameter  and  depth  of  the  crater,  the 
length  of  the  arc  and  the  diameter  of  the  knob  of  the  negative 
carbon  under  varying  circumstances,  and  he  found  that  "  the 
arc  burns  away  the  carbons  so  as  to  keep  all  points  at  an  equal 
distance  from  each  other."83  He  considered  that  the  sudden 
diminution  of  the  P.D.  between  the  carbons  when  hissing  began 
was  due  to  the  dampening  effect  of  the  cool  carbon  preventing 
the  consumption  of  energy.84 


04  THE  ELECTRIC  AEC. 

In  1892  Stenger  sought  for  evidence  of  a  back  E.M.F.  in 
the  arc  thus :  A  shunt-dynamo  sent  a  current  through  an 
arc,  5  accumulators,  and  a  tangent  galvanometer,  in  series. 
The  accumulators  were  joined  up  so  as  to  oppose  the  current,  and 
the  needle  of  the  galvanometer  was  pressed  against  a  stop  so 
that  it  was  not  deflected  by  the  dynamo  current,  but  could  move 
freely  in  the  opposite  direction.  On  short-circuiting  the  shunt- 
dynamo  the  conduction  of  the  arc  lasted  long  enough  for  the 
accumulators  to  send  a  current  and  produce  a  deflection  of 
over  90deg.  in  the  galvanometer ;  but,  when  the  experiment 
was  repeated  with  the  accumulators  removed  from  the  circuit, 
a  deflection  of  only  about  fdeg.  occurred,  produced  by  the 
spring  of  the  stop.  Hence  any  back  E.M.F.  in  the  arc  either 
ceased  with  the  main  current,  or  was  very  small  compared  with 
10  volts.86 

In  a  Paper  read  before  the  British  Association  in  1892,  Prof. 
Silvanus  Thompson  gave  an  approximate  formula  connecting 
V,  the  P.D.  in  volts  between  the  carbons,  /,  the  length  of  the 
arc  in  millimetres,  and  A,  the  current  in  amperes,  viz.  : — 

bl 
V-«  +  T 

where  the  constant  a,  however,  varied  between  35  and  39 
volts  and  the  constant  b  between  8  and  18.  The  constant 
part  of  the  P.D.  which  is  independent  of  the  current  for  an 
invariable  length  is  sometimes  called  the  apparent  back 
E.M.F.,  and,  although  Dr.  Thompson  did  not  affirm  that  there 
was  an  actual  back  E.M.F.,  he  considered  that  the  arc  acted 
as  though  it  were  the  seat  of  a  back  E.M.F. 

He  described  his  experiments,  made  with  an  auxiliary 
exploring  carbon,  which  showed  that  the  drop  of  potential  in 
the  arc  itself  was  small,  and  that  the  main  drop  was  at  the 
positive  carbon.  The  latter,  he  considered,  was  accounted  for 
by  the  volatilisation  of  the  carbon  at  the  crater,  which,  he 
suggested,  was  always  at  the  temperature  of  boiling  carbon, 
und  this  idea  was  confirmed,  he  thought,  by^Bapt.'  Abney's 
discovery  that  the  brilliancy  of  the  same  o.uaU£y  of  car- 
bon per  square  centimetre  was  a  constant.  A&&-  Crookes's 
experiments,  which  showed  that  the  flaming  discharges 
produced  by  very  high- pressure  very  short  period  alterna- 


A  SHOUT  HISTOEY  OF  THE  AUG.  65 

ting  currents  were  endothermic  flames  of  nitrogen 
and  oxygen,  had  led  hhn  to  try  whether  the  combination  of 
nitrogen  and  oxygen  produced  by  the  high  temperature  of  the 
arc  had  anything  to  do  with  the  E.M.F.  observed  there. 
To  test  this  he  surrounded  the  arc  with  a  glass  tube,  and 
introduced  successively  oxygen,  nitrogen,  carbon  dioxide, 
hydrogen,  &c.,  but  with  a  normal  arc  taking  10  amperes  not 
one  volt  difference  in  the  P.D.  was  observed.  When  chlorine 
or  carbon  monoxide  surrounded  the  arc  the  positive  carbon  was 
flattened  over  the  end,  and  the  end  of  the  negative  became  a 
very  obtuse  cone,  while  with  hydro-carbon  gas  the  crater  was 
very  deep;  and,  lastly,  when  the  arc  was  formed  in  oxygen 
the  carbons  burnt  away  very  rapidly.  The  gases  had  to  be 
introduced  quietly,  since  blowing  on  an  arc  in  ordinary  air 
Dr.  Thompson  found  raised  the  P.D.  to  75  volts.87 

Later  in  the  same  year  M.  Violle  published  an  account  of 
some  experiments  he  had  made  in  order  to  determine  the 
temperature  of  the  positive  carbon  and  the  arc. 

He  cut  a  deep  trench  all  round  the  positive  carbon  a  little 
way  from  the  end,  so  that  a  small  piece  was  left,  only  con- 
nected with  the  rest  of  the  carbon  by  a  narrow  neck.  When 
most  of  this  piece  was  burnt  away,  and  the  remainder  was  all 
of  the  same  brightness,  it  was  shaken  off,  and  fell  into  a  little 
cup,  after  which  the  amount  of  heat  given  off  by  it  was 
measured  in  the  usual  way.  Assuming  the  ordinarily  received 
value  of  the  specific  heat  of  carbon,  M.  Violle  found  by  this 
method  that  the  temperature  of  the  crater  was  about 
3,500°C.,  whatever  power  was  spent  in  the  arc — whether  10 
amperes  were  flowing  at  50  volts,  or  400  amperes  at  85  volts. 
He  concluded,  therefore,  that  the  candle-power  per  square 
centimetre  of  the  crater  was  the  same  for  all  arcs  with  the 
same  kind  of  carbons.88 

In  1893  M.  Violle  made  some  further  experiments  on  the 
temperature  and  brightness  of  the  crater.  The  carbons  were 
placed  horizontally,  and  inclosed,  in  order  to  reduce  the  cooling 
effect  of  the  surrounding  air.  The  temperature  was  measured 
in  the  same  way  as  in  his  previous  experiments,  and  led  to  the 
same  result,  namely,  that  the  temperature  of  the  crater  was 
about  3,500°C.  He  considered  that  the  arc  itself  was  at  the 
same  temperature,  and  that  this  was  the  temperature  of  boiling 


66  THE  ELECTRIC  AEC. 

carbon.  He  laid  great  stress  on  this,  as  may  be  seen  from 
the  following  quotation  :  "  The  most  important  result  of  my 
researches  is  to  establish  the  fact  that  the  voltaic  arc  is  the 
seat  of  a  perfectly  definite  physical  phenomenon,  the  ebullition 
of  carbon." 

To  determine  the  amount  of  light  given  out  per  square  milli- 
metre of  crater  he  employed  two  methods,  (1)  the  use  of  the 
spectrophotometer,  (2)  photography.  They  both  led  him  to  the 
same  conclusion,  that  the  amount  of  light  per  square  mm.  was 
constant,  and  independent  of  the  current  used. 

Finally  M.  Violle  gave  reasons  for  believing  that  the  arc  is 
an  electrolytic  phenomenon,  in  which  there  is  a  continual  stream 
of  carbon  vapour  passing  from  the  positive  to  the  negative 
electrode.89 

In  August,  1893  Messrs.  Duncan,  Rowland  and  Todd  pub- 
lished an  account  of  the  effects  they  had  obtained  on  producing 
an  arc  under  pressure  and  in  a  vacuum.  They  began  their 
Paper  by  stating  that  the  two  causes  alleged  for  the  back 
E.M.F.  in  the  arc  —  the  vaporisation  of  the  positive  pole  and 
the  thermo-electric  effect  produced  by  the  carbon  vapour  in 
contact  with  the  unequally  heated  carbons  —  must  both  be 
operative  ;  but  that  the  first  must  cease  to  exist  directly  the 
main  current  ceased  to  flow,  and  could  not  therefore  be  detected 
even  immediately  after  the  circuit  was  broken,  while  they  con- 
sidered it  must  be  possible  to  detect  evidence  of  the  latter  for 
a  short  time  after  the  main  current  had  been  stopped. 

The  first  part  of  the  back  E.M.F.  ,  viz.,  that  due  to  the 
volatilisation  of  the  carbon,  they  considered  must  be  a  constant 
a,  while  the  second  part  must  be  a  function  of  the  current  and 
the  length  of  the  arc.  From  these  considerations  they  sug- 
gested that  the  complete  equation  connecting  P.D.,  current,  and 
length  of  arc  should  be 


where  V  was  the  P.D.  between  the  carbons,  I  the  length  of  the 
arc,  and  A  the  current. 

They  next  called  attention  to  the  fact  that  the  P.D.  between 
the  carbons  diminished  as  the  current  increased,  and  gave  the 
results  of  experiments  supporting  this.  The  following  they 
suggested  as  an  explanation  of  the  phenomenon.  If  V  be  the 


A  SHORT  HISTORY  OF  THE  ARC.  67 

P.D.  between  the  carbons,  a  the  constant  back  E.M.F.  due  to 
volatilisation  of  the  carbon,  and  a  the  back  E.M.F.  due  to 
thermo-electric  action, 

V  -  a  -  of 


Now,  a'  diminishes  with  increase  of  current,  since  the  tem- 
perature of  the  negative  carbon  increases  while  that  of  the 
positive  remains  constant.  Hence  V  diminishes  as  A  increases. 

Keeping  the  current  constant  at  six  amperes,  and  the  arc  of 
a  fixed  length,  they  found  that,  starting  with  the  atmospheric 
pressure,  V  increased  as  the  pressure  was  increased,  but  at  a 
slower  rate.  When,  on  the  other  hand,  the  pressure  of  the 
surrounding  air  was  reduced  below  that  of  the  atmosphere, 
V  also  increased  except  in  the  case  of  the  T\th-inch  arc 
when  V  diminished  on  reducing  the  pressure.  This  except 
tional  result,  however,  arose  probably  from  the  arc  hissing. 
Hence,  for  a  given  current  and  length  of  silent  arc,  V  has  a 
minimum  value  for  atmospheric  pressure.  The  increase  of  V 
as  the  pressure  was  reduced  below  that  of  the  atmosphere  they 
considered  was  caused  by  an  increase  of  a',  for  they  said  that  a, 
the  constant  counter  E.M.F.,  was  probably  lower  in  a  vacuum, 
and  the  positive  carbon  not  so  hot,  but  the  negative  carbon 
seemed  to  cool  proportionately  faster  than  the  positive. 

The  counter  E.M.F.,  they  concluded,  increased  apparently 
with  the  pressure  above  one  atmosphere,  while  the  ohmic  resist- 
ance of  the  arc  did  not  greatly  change.  As  regards  the  formula, 
their  experiments  showed  that  a  varied  with  I  for  each  pressure 
employed,  and  they  failed  to  arrive  at  any  exact  law  connecting 
V,  I  and  A,  even  for  one  pressure,  the  equation  that  most 
nearly  fitted  their  results  being,  they  thought, 


but  this,  they  remarked,  was  only  approximately  correct.90 

In  some  articles  published  in  1893  M.  Blondel  gave  it  as  his 
experience  that,  although  the  maximum  brilliancy  of  the  crater 
was  independent  of  the  current  flowing  in  the  arc,  yet  that  the 
average  brilliancy  of  the  incandescent  portions  increased  both 

F2 


68  THE  ELECTEIC  ARC. 

with  the  intensity  and  with  the  density  of  the  current,  until 
the  crater  was  well  saturated.  If,  he  said,  the  value  of  the 
current  be  suddenly  varied,  the  intrinsic  brilliancy  undergoes  a 
temporary  and  very  appreciable  variation  which  may  reach  ten 
per  cent.,  and  which  diminishes  gradually  until  the  dimensions 
of  the  crater  are  so  altered  as  to  restore  the  surface  of  emission 
to  the  value  that  it  ought  to  have  for  the  new  current.  He 
considered  that  the  heating  of  the  crater  only  took  place  at  the 
surface,  and  that  the  temperature  of  volatilisation  was  only 
reached  by  a  very  thin  superficial  film. 

In  order  that  the  light  of  the  crater  should  not  vary  with 
the  carbons  employed,  he  was  of  opinion  that  it  was  necessary 
that  the  carbons  should  contain  a  very  small  admixture  of 
foreign  substances,  and. that  the  molecular  condition  of  the 
light  giving  surface  should  be  always  the  same.  He  thinks 
that  the  surface  of  the  crater  is  always  turned  into  graphite 
with  carbon  electrodes,  so  that  they  always  fulfil  the  second 
condition.  He  found  the  intrinsic  brilliancy  of  the  crater  to- 
vary  between  152  and  163  "bougies  decimales." 

With  the  hissing  arc  M.  Blondel  observed  that  the  current 
flowed  jerkily,  the  violet  part  of  the  arc  became  blue-green,  and 
the  arc  lost  its  transparency,  being  transformed  into  an  incan- 
descent mist  that  hid  the  crater.  When  hissing  ceased,  and  the 
arc  became  violet  again,  he  noticed  that  the  crater  appeared  to- 
be  covered  with  black  specks  which  gradually  disappeared,  a 
fact  which  he  thought  pointed  to  a  lowering  of  the  temperature 
during  hissing.  The  arc  while  hissing  gave  from  10  to  20  per 
cent,  less  light  than  when  silent,  and  M.  Blondel  concluded 
therefore  that  while  with  the  silent  arc  most  if  not  all  of  the 
carbon  that  is  transferred  from  one  pole  to  the  other  is  volati- 
lised, with  the  hissing  arc  a  large  part  of  it  is  transferred  by 
disruptive  discharge.91 

In  1894  M.  Violle  renewed  his  inquiries  into  the  temperature 
of  the  arc  with  a  still  larger  range  of  current  than  before, 
namely,  10  to  1,200  amperes.  He  found  that  in  all  cases  the 
temperature  and  intrinsic  brilliancy  of  the  positive  carbon 
remained  constant.  The  arc  he  employed  was  enclosed,  and  he 
found  by  spectroscopic  methods  that  the  brilliancy  of  the  arc 
itself  increased  as  the  current  increased.  While  doubting  that 
the  brilliancy  of  luminous  rays  contributing  to  the  spectra  of 


A  SHORT  HISTORY  OF  THE  ARC.  69 

gases  was  connected  with  the  temperature  by  the  same  relation 
as  the  brilliancy  of  the  corresponding  regions  in  spectra  of  solid 
bodies,  he  still  considered  that  his  experiments  led  to  the  con- 
clusion that  the  temperature  of  the  arc  proper  increased  with 
the  current,  and  was  in  general  higher  than  that  of  the  positive 
carbon.92 

In  the  same  year,  while  experimenting  with  a  view  to  using 
a  fixed  portion  of  the  supposed  uniform  light  of  the  crater  of 
an  arc  as  a  practical  standard  of  light,  Mr.  Trotter  made  his 
notable  discovery  of  the  rotation  of  the  arc.  By  the  use  of  a 
double  Rumford  photometer,  giving  alternating  fields,  as  in  a 
Vernoa  Harcourt  photometer,  his  attention  was  called  to  a 
bright  spot  at  or  near  the  middle  of  the  crater.  The  use  of  rotat- 
ing sectors  accidentally  revealed  that  a  periodic  phenomenon 
accompanied  the  appearance  of  this  bright  spot,  and  though  it 
is  more  marked  with  a  short  humming  arc,  the  author  believes 
that  it  is  always  present. 

An  image  of  the  crater  was  thrown  on  to  a  screen  by  a  photo- 
graphic lens  ;  and  a  disc  having  60  arms  and  60  openings  of 
3°,  and  rotating  at  from  100  to  400  revolutions  per  minute,  was 
placed  near  the  screen.  Curious  stroboscopic  images  were 
observed,  indicating  a  continually  varying  periodicity,  seldom 
higher  than  450  per  second,  most  frequently  about  100, 
difficult  to  distinguish  below  50  per  second,  and  becoming  with 
a  long  arc  a  mere  nicker.  The  period  seemed  to  correspond 
with  a  musical  hum  of  the  arc,  which  generally  broke  into  a 
hiss  at  a  note  a  little  beyond  450  per  second.  The  hum  was 
audible  in  a  telephone  in  the  circuit,  or  in  shunt  with  it.  The 
current  was  taken  from  the  mains  of  the  Kensington  and 
Knightsbridge  Electric  Light  Company,  often  late  at  night, 
after  all  the  dynamos  had  been  shut  down.  The  carbons  were 
not  cored  ;  six  kinds  were  used. 

A  rotating  disc  was  arranged  near  the  lens,  to  allow  the 
beam  to  pass  for  about  yj^th  of  a  second,  and  to  be  cut  off 
for  about  yj^th  of  a  second.  It  was  then  found  that  a 
bright  patch,  occupying  about  one-quarter  of  the  crater, 
appeared  to  be  rapidly  revolving.  Examination  of  the  shape 
of  this  patch  showed  that  it  consisted  of  the  bright  spot  already 
mentioned,  and  of  a  curved  appendage  which  swept  round, 
sometimes  changing  the  direction  of  its  rotation.  This  appen- 


70  THE  ELECTRIC  ARC. 

dage  seemed  to  be  approximately  equivalent  to  a  quadrant 
sheared  concentrically  through  90°. 

The  author  inclined  to  the  theory  of  constant  temperature  of 
the  arc,  and  attributed  this  phenomenon,  not  to  any  actual 
change  in  the  luminosity  of  the  crater,  or  to  any  wandering  of 
the  luminous  area,  such  as  is  seen  with  a  long  unsteady  arc, 
but  to  the  refraction  of  the  light  by  the  heated  vapour.  All 
experiments,  such  as  enclosing  the  arc  in  a  small  chamber  of 
transparent  mica,  or  the  use  of  magnets,  or  an  air  blast, 
failed  to  produce  any  effect  in  altering  the  phenomenon.  A 
distortion  of  the  image  of  the  crater  while  the  patch  revolved 
was  looked  for,  but  nothing  distinguishable  from  changes  of 
luminosity  was  seen.03 


FIG.  19. 

Prof.  Fleming,  in  the  course  of  experiments  on  the  arc  in 
1894,  was  led  to  believe  that  the  carbon  boiled  at  the  crater, 
and  that  the  violet  core  of  the  arc  consisted  of  a  torrent  of 
carbon  vapour  passing  towards  the  negative  pole.  This  violet 
core  may  be  heated  to  a  higher  temperature  than  that  of  the 
crater  by  the  passage  of  the  current  through  it.  He  thought 
that  at  the  cooler  negative  pole  some  of  the  carbon  vapour  was 
condensed,  but  that  some  of  it  was  deflected  back  again  on  to 
the  positive  carbon,  "  causing  the  golden  aureole  or  flame  and 
creating  thus  a  double  carbon  current  in  the  arc."  The  negative 
carbon,  he  thought,  gave  evidence  after  use  of  having  been  worn 
away  by  a  kind  of  sand  blast  action. 


A  SHORT  HISTORY  OF  THE  ARC.  71 

Joining  the  positive  carbon,  an  electric  bell,  and  a  third  car- 
bon which  dipped  into  the  arc,  in  series,  he  found  that  sufficient 
current  passed  in  the  circuit  to  make  the  bell  ring,  but  if  the 
negative  carbon  were  jomed  up  instead  of  the  positive,  the  bell 
gave  no  sound.  This  led  him  to  conclude  that  there  was  no 
perceptible  P.D.  between  the  arc  and  the  negative  carbon. 

Fig.  19  shows  the  arrangement  used  by  Prof.  Fleming  in 
experimenting  on  the  conductivity  of  the  arc. 

The  third  carbon  T,  upon  which  the  arc  was  made  to  play 
steadily  by  means  of  the  magnet,  was  joined  up  in  series  with 
the  galvanometer  G,  the  battery  of  15  secondary  cells  B,  and 
the  negative  carbon.  When  the  negative  pole  of  the  battery  was 
joined  to  the  negative  carbon  the  galvanometer  needle  was 
deflected,  showing  that  a  current  was  passing,  but  when  the 
poles  of  the  battery  were  reversed  there  was  no  deflection  of  the 
galvanometer.  Hence  Prof.  Fleming  concluded  that  the  arc 
possessed  a  unilateral  conductivity,  allowing  a  negative  current 
to  flow  through  it  from  the  negative  carbon  to  the  positive,  but 
not  allowing  a  positive  current  to  flow  in  the  same  direction. 
After  performing  this  experiment  it  was  found  that  the  third 
carbon  T  was  cratered,  and  that  its  tip  was  converted  into 
graphite.94 

A  measurement  of  what  was  considered  to  be  the  true 
resistance  of  the  arc  was  made  in  1895  by  Mr.  Julius  Frith 
with  the  Wheatstone's  bridge  seen  in  Fig.  20.  Two  of 
its  arms,  P,  Q,  consisted  of  the  two  halves  of  a  stretched  platinoid 
wire,  each  having  a  resistance  of  5 -35  ohms.  The  third  arm  was 
composed  of  a  battery  of  26  accumulators,  E,  which,  together 
with  a  shunt  dynamo  D^  sent  a  current  through  a  resistance, 
RU  an  ammeter  C  and  the  arc  X  in  series,  the  arc  being 
2mm.  in  length,  formed  with  carbons  llmm.  in  diameter.  The 
fourth  arm  consisted  of  a  shunt  dynamo,  D2,  exactly  similar 
to  D1?  only  at  rest,  together  with  resistances  R2  and  R3  and 
a  coil  L,  whose  self-induction  could  be  varied  by  moving  an 
iron  core. 

The  resistances  of  Dx  and  D2  were  each  0-04  ohm  ;  of  Rj  and 
R2,  each  8  ohms  ;  of  E,  0*25  ohm  ;  and  of  R3  0'3  ohm. 

Before  closing  the  switch  S,  the  speed  of  the  dynamo  Dj 
and  the  length  of  the  arc  were  varied  until  the  potential  of 
the  points  A  and  B  were  equal,  as  tested  by  the  voltmeter  V, 


72  THE  ELECTRIC  ARC. 

which,  by  means  of  the  switch  K,  could  be  connected  either 
across  the  accumulators  E  or  across  the  arc  X. 

An  alternator  D3  sent  an  alternating  current  through  a 
wire,  any  two  points  of  which  could  be  tapped  to  supply  the 
alternating  P.D.  to  the  bridge,  and,  after  closing  the  switch  S, 
the  resistance  of  R3  and  the  self-induction  of  L  were  varied 
until  the  sound  in  the  telephone  T  became  a  minimum,  the 
condenser  M,  inserted  in  the  telephone  circuit,  cutting  off'  from 
the  telephone  any  direct  current  effect  that  might  be  caused 
by  want  of  perfect  equalisation  of  the  potentials  of  the  points 
A  and  B. 

The  best  results  were  obtained  with  R8  having  a  resistance 
of  about  0'6  ohm,  and  an  alternating  P.D.  of  5  volts  supplied  to 
the  bridge.  This  makes  the  resistance  of  the  arc  about  0*6  ohm, 
which,  together  with  the  readings  of  the  ammeter  C  and  the 
voltmeter  V,  give  the  back  E.M.F.  in  the  arc  as  39  volts. 

Other  methods  of  testing  were  employed  by  Mr.  Frith,  and 
results  were  obtained  agreeing  with  the  above.95 

Mr.  Wilson  has  experimented  on  the  electric  arc  under 
considerable  atmospheric  pressures.  As  the  pressure  was 
increased,  and  the  current  kept  constant,  he  found  that  the 
apparent  resistance  of  the  arc  increased.  When  the  pressure 
had  been  raised  to  five  atmospheres  the  temperature  of  the 
crater  had  fallen,  while  at  20  atmospheres  the  brilliancy  of  the 
crater  fell  to  a  dull  red  colour.  Diminishing  the  pressure,  on 
the  contrary,  increased  the  brightness. 

Mr.  Wilson  therefore  concluded  that  "the  temperature  of 
the  crater,  like  that  of  the  filament  in  an  incandescent  lamp, 
depends  on  how  much  it  is  cooled  by  the  surrounding  atmos- 
phere, and  not  on  its  being  the  temperature  at  which  the 
vapour  of  carbon  has  the  same  pressure  as  the  surrounding 
atmosphere."97 

Mr.  Freedman  made  some  experiments  on  "  The  Counter 
Electromotive  Force  in  the  Electric  Arc,"  using  small  currents 
up  to  two  amperes,  with  electrodes  of  different  substances.  His 
conclusions  were  as  follows  : — 

"  1st.  There  is  a  counter  E.M.F.  present  in  an  electric  arc 
depending  simply  upon  the  material  and  temperature  of  volatili- 
sation of  the  electrodes,  and  this  counter  E.M.F.  has  a  constant 
definite  value  for  that  material. 


A  SHOET  HISTORY  OF  THE  ARC. 


74  THE  ELECTRIC  AEG. 

"  2nd.  On  account  of  the  different  temperatures  there  must 
be  a  thermo-electric  effect.  The  counter  E.M.F.  due  to  this 
phenomenon  must  depend  on  the  difference  of  temperature  be- 
tween the  electrodes.  Consequently,  it  must  increase  with  the 
length  of  the  arc  as  the  temperature  of  the  negative  electrode 
falls  ;  and  it  must  decrease  with  the  current  as  the  temperature 
of  the  negative  electrode  rises. 

"  3rd.  It  is  fair  to  assume  that  two  amperes  of  current  will 
tear  off  twice  as  many  molecules,  in  the  same  length  of  time, 
from  the  positive  electrode  as  one  ampere  ;  in  strict  analogy 
to  electro-deposition.  If  the  quantity  of  matter  is  doubled  the 
resistance  is  most  likely  halved  ;  so  that  c  R  would  remain  a 
constant  quantity.  This  would  be  so,  provided  the  temperature 
remained  constant.  But  since  the  temperature  rises  with 
increase  of  current,  c  R  must  actually  decrease  with  increase 
of  current." 

From  these  considerations  Mr.  Freedman  formed  the  follow- 
ing "  complete  formula  for  the  difference  of  potential  between 
the  electrodes." 


in  which 

n?  =  the  constant  counter  E.M.F.,  depending  upon  the  material 
of  the  electrodes  and  its  temperature  of  volatilisation. 

y  =  the  counter  E.M.F.  due  to  the  thermo-electric  effect,  being 
a  function  of  the  material  of  the  electrodes  and  the  differ- 
ence of  the  temperature;  the  higher  temperature  being 
that  of  volatilisation  of  the  electrode  and  the  lower  depend- 
ing upon  the  material  and  size  of  the  electrode,  the  current 
and  the  length  of  the  arc. 

c  =  the  current  strength. 

R  =  the  ohmic  resistance  of  the  arc,  depending  upon  the  material 
of  the  electrodes,  the  length  of  the  arc,  the  temperature 
and  the  current. 
For  any  given  material  of  electrodes  analytically  expressed 

in  terms  of  length  and  current,  said  the  author, 

v  =  x+f  (I,  c)  +  c/'  (I,  c) 
or  in  terms  of  temperature  and  currents, 


At  the  meeting  of  the  British  Association  at  Ipswich  in  1895, 


A  SHORT  HISTORY  OF  THE  ARC.  75 

Prof.  Ayrton  read  a  short  Paper  on  "The  Resistance  of  the  Arc." 
He  had  been  led,  by  the  study  of  the  various  curves  connecting 
the  P.D.  between  the  carbons  with  the  current  flowing  for  con- 
stant lengths  of  arc,  to  the  conclusion  that  if  there  were,  as  most 
observers  seemed  to  think,  a  back  E.M.F.  and  a  true  resistance 
in  the  arc,  then  the  resistance  must  be  negative.  Some  experi- 
ments made  by  Mr.  Mather  at  his  suggestion  strengthened  the 
idea.* 

"  In  one  of  these  experiments  two  points  of  equal  potential 
were  found  in  a  circuit  consisting  of  an  arc,  a  battery,  and  a 
resistance.  Another  battery,  consisting  of  a  few  cells  of  known 
E.M.F.  and  resistance  was  applied  between  these  two  equi- 
potential  points,  and  the  current  flowing  through  the  battery 
was  noted.  The  resistances  of  the  two  parallel  halves  of  the 
circuit,  excluding  the  arc,  were  known,  so  that  the  current 
which,  taking  the  arc  resistance  as  zero,  should  flow  through 
this  battery,  could  be  calculated.  Now  the  value  of  this  calcu- 
lated current  was  found  to  be  less  than  the  observed  value,  no 
matter  in  which  direction  the  P.D.  was  applied,  and  this  result 
was  also  obtained  when  an  alternating  P.D.  was  used.  Hence 
the  resistance  of  the  arc  was  apparently  less  than  zero." 

"The  other  experiment  consisted  in  running  the  arc  at  a 
steady  P.D.  and  current,  suddenly  altering  the  resistance  in 
circuit  by  a  small  amount,  and  noting  the  changes  in  the 
ammeter  and  voltmeter-readings  so  produced.  The  new  con- 
ditions were  maintained  only  long  enough  to  allow  of  these 
readings  being  taken.  The  arc  was  then  brought  back  to  its 
former  condition  before  taking  another  reading.  It  was  found 
that  a  change  of  P.D.  in  one  direction  was  always  accompanied 
by  a  change  of  current  in  the  opposite  direction.  The  results 
of  both  experiments  were  however  only  qualitative." 

It  may  be  mentioned,  that  although  the  idea  of  a  negative 
resistance  in  the  arc  occurred  to  Prof.  Ayrton  quite  indepen- 
dently, before  he  had  ever  heard  of  Luggin's  work  on  the 
subject,  yet  that  able  experimenter  made  the  same  suggestion 
as  long  ago  as  1888  (see  p.  54). 

In  their  Paper  read  before  the  Physical  Society,  in  May, 

*  Prof.  Ayrlon's  Paper  was  not  published,  but  the  account  of  it  given 
here  is  taken  from  the  Paper  on  the  same  subject  read  by  Messrs.  Frith 
and  Rodgers,  before  the  Physical  Society,  in  May,  1896. 


76 


THE  ELECTRIC  AEC. 


1896,  Messrs.  Frith  and  Rodgers  gave  the  results  of  a  long  and 
very  complete  series  of  "  Experiments  on  the  Eesistance  of  the 
Arc,"  undertaken  with  a  view  to  throwing  some  light  on  the 
discrepancy  between  the  negative  resistance  obtained  by  Prof. 
Ayrton  and  the  positive  resistance  found  by  all  other 
experimenters.  They  tried  several  methods  of  experimenting, 
the  most  successful  of  which  is  represented  diagrammatically 
in  Fig.  21. 

D  is  the  armature  of  an  alternator,  the  current  from  which 
passes  round  two  circuits  in  parallel,  one  of  which  contains  the 
arc  X,  and  the  other  an  adjustable  resistance  R.  By  adjusting 
R  the  alternating  currents  in  the  two  halves  can  be  made  equal. 


When  this  is  the  case  the  impedances  of  the  two  halves  to 
alternating  currents  must  be  equal. 

The  continuous  current  circuit  shown  to  the  left  consists  of 
a  battery  of  accumulators  B,  the  hand-adjusted  arc  lamp  X, 
the  resistance  K,  the  ammeter  A,  and  (with  the  commutator  0 
as  shown)  the  resistance  S  and  the  alternator  D.  The  alter- 
nator D  carries  the  continuous  current,  but  this  does  not 
prevent  its  acting  as  an  alternator. 

The  air  transformer  T  was  used  to  measure  the  small  alter- 
nating current  independently  of  the  continuous  current  flowing. 
For  this  purpose  its  thick  wire  coil  was  placed  in  series  with 


A  SHORT  HISTORY  OF  THE  ARC.  77 

the  alternator  D,  and  its  thin  wire  coil  was  connected  with  an 
electrostatic  voltmeter  E.  By  means  of  the  commutator  C,  the 
air-transformer  T  could  be  thrown  into  either  circuit,  the  resis- 
tance S  being  thrown  by  the  same  operation  into  the  other 
circuit.  The  resistance  S  was  equal  to  that  of  the  thick  wire 
coil  of  T,  so  that  when  S  replaced  T  the  continuous  current 
was  unaffected  by  the  change. 

When  experimenting,  the  arc  was  run  at  the  required  current 
and  P.D.  by  altering  the  number  of  cells  in  B,  K  being  always 
kept  the  same.  R  was  then  adjusted  till  the  deflection  of  E 
was  the  same  when  T  was  in  either  circuit.  If  the  value  of  R 
when  balance  was  obtained  were  R1?  then 

^^k  +  bi  +  l  +  x (i) 

where  k  was  the  constant  resistance  at  K,  bl  was  the  resistance 
to  alternating  currents  of  the  battery  B,  I  the  resistance  of  the 
arc  lamp  and  connections,  and  x  the  resistance  of  the  arc. 

The  carbons  were  next  firmly  screwed  together  and  the  number 
of  cells  in  B  reduced,  till  the  continuous  current  was  the  same 
as  before.  R  was  again  adjusted  till  the  deflections  of  E  were 
equal,  then  if  R2  were  the  new  value  of  the  resistance,  and  b2 
the  resistance  of  the  portion  of  the  battery  now  used 

-R2  =  h  +  b2  +  l (ii). 

Next  the  cells  were  cut  out  and  the  mains  leading  to  them  were 
short  circuited,  so  that  the  third  value  of  R  obtained  was 

R3-£  +  Z (Hi). 

From  (ii)  and  (iii)  the  resistance  of  b2  was  obtained,  and,  by 
proportion,  of  any  number  of  cells.  Putting  these  values  in  (i) 
the  value  of  x  in  ohms  was  found. 

Messrs.  Frith  and  Rodgers  defined  the  resistance  of  the 
arc  as  the  ratio  of  a  small  increment  of  P.D.  applied,  to  the 
small  increment  of  current  produced ;  that  is,  they  were 

measuring  the  value  of  -TT-  when  an  alternating  current  was 
applied  to  the  arc  which  they  considered  to  be  too  small  to 
produce  any  visible  effect  on  it.  They  called  this  the  "instan- 
taneous" -j-r  to  distinguish  it  from  the  steady^-;  the  tangent 

of  the  inclination  of  the  tangent  line  to  the  curve  representing 
the  steady  values  of  V  and  A  with  a  constant  length  of  arc. 


78  THE  ELECTRIC  ARC. 

In  order  to  show  the  difference  between  these  two  values, 
and  also  to  show  that  in  an  analogous  case,  where  the  resistance 
could  be  measured  apart  from  the  back  E.M.F.,  the  instantaneous 

dV 

-V-T-  found  by  superimposing  a  small  alternating  current  on  a 

CL  A. 

continuous  one  did  really  give  the  value  of  the  resistance,  a 
glow  lamp  taking  a  current  of  10  amperes  at  a  P.D.  of  about 
8  volts  was  joined  in  series  with  three  accumulators.  Thus, 
they  had  a  resistance  which  they  could  measure  separately  in 
series  with  a  back  E.M.F.  They  then  sent  a  small  alternating 
current  through  the  circuit  against  the  E.M.F.  of  the  accumu- 
lators, and  plotting  the  curve  obtained  for  the  instantaneous 

dV 

—  and  current,  they  found  it  very  nearly  coincided  with  the 

curve  representing  the  observed  resistance  and  the  current, 
while  the  values  found  for  the  steady  -y-  were  all  smaller  than 

the  corresponding  resistances. 

This  experiment,  the  authors  considered,  justified  them  in 
concluding  that  if  the  arc  consists  of  a  back  E.M.F.  and  a 
resistance,  the  actual  value  of  the  resistance  was  given  by  their 
method. 

They  varied  the  conditions  of  their  experiments  as  much  as 
possible.  They  studied  the  effect  on  the  resistance  of  the  arc 
of  variations  in  the  amount,  frequency,  and  wave  form  of  the 
alternating  current ;  the  effect  of  different  kinds  of  carbons  and 
different  P.Ds.  and  currents ;  the  effect  of  using  different  com- 
binations of  cored  and  solid  carbons,  of  carbons  cored  with 
substances  other  than  carbon,  and  the  effect  of  the  relative  sizes 
of  the  carbons. 

The  largest  alternating  current  used  had  a  root  mean  square 
value  equal  to  about  10  per  cent,  of  the  continuous  current. 
Frequencies  between  the  limits  of  250  and  7  complete  alterna- 
tions per  second  had  no  effect  on  the  resistance  of  the  arc. 
Complete  information  respecting  the  carbons  is  given  in  the 
figures.  It  will  be  seen  from. these  that  the  ordinates  of 
+  solid  -  solid  are  all  negative,  those  of  +  cored  -  cored  are  all 
positive,  and  that  the  other  curves  all  lie  between  these  two 
extremes.  The  curves  in  Fig.  22  connect  resistance  with  cur- 
rent for  a  constant  P.D. ;  those  in  Fig.  23  connect  resistance 
and  P.D.  for  a  constant  current.  The  curves  for  solid  carbons 


A  SHORT  HISTORY  OF  THE  ARC. 


79 


are  in  each  case  all  very  close  together,  while  those  for  which 
cored  carbons  were  used  show  much  greater  divergence  owing 


0 


ve. 


-2 


Current  in  Amperes. 
FIG.  22. 

to  variations  in  the  formation  and  diameter  of  the  cores  with 
different  makes  of  carbons. 


80 


THE  ELECTRIC  ARC. 


From  the  curves  the  authors  concluded  that  with  both 
carbons  solid  the  resistance  of  the  arc  was  always  negative  • 
with  both  cored  it  was  always  positive,  and  with  one  cored  and 


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Resistance  of  the  Arc  in  Ohms. 


A  SHOET  HISTORY  OF  THE  ARC.  SI 

the  other  solid  it  was  sometimes  positive  and  sometime* 
negative. 

They  pointed  out  that  with  a  constant  current  the  resistance 
of  the  arc  appeared  always  to  reach  a  minimum  as  the  arc  was 
lengthened  out,  and  then  to  increase  again.  This  minimum  is 
more  strongly  marked  and  occurs  with  a  smaller  P.D.  with 
cored  than  with  solid  carbons.  It  is  reached  with  cored  carbons 
with  the  shortest  arc  in  which  the  dark  central  space  appears 
(see  p.  7). 

With  inverted  arcs  the  resistance  with  solid  carbons  was 
practically  unchanged,  but  with  cored  carbons  no  dark  space 
was  seen,  and  the  resistance  was  much  less  than  for  ordinary 
arcs.  The  authors  considered  that  the  degree  of  contact 
between  the  purple  glow  and  the  negative  carbon  had  great 
effect  on  the  resistance  of  the  arc,  which  was  most  negative 
when  that  contact  was  most  perfect. 

When  both  carbons  were  cored   it    was  found   that  above 

a  certain  frequency  the  instantaneous  —    was   positive,  and 

uA 

below  that  frequency  it  was  negative.  The  critical  frequency 
was  about  1/8.  With  the  positive  carbon  cored  and  the  negative 
solid,  at  35  volts  the  resistance  was  positive  with  all  frequen- 
cies, at  45  volts  it  was  negative  with  all  frequencies,  and  at  55 
volts  it  was  positive  with  frequencies  above  1/8,  and  negative 
with  frequencies  below  that. 

The  authors  found  that  the  current  flowing  through  a  hissing 
arc  was  oscillatory,  the  oscillatory  current  amounting  in  one 
case  to  3  per  cent,  of  the  continuous  current.103 

Arons  made  some  fresh  experiments  in  1896  to  prove  the 
existence  of  a  back  E.M.F.  in  the  arc,  and  to  determine  its 
value.  He  worked  on  the  same  lines  as  Stenger  (see  p.  64), 
using,  however,  the  town  mains,  which  gave  105  to  110  volts, 
instead  of  a  dynamo.  His  arrangement  was  as  follows. 

The  mains  (Fig.  24)  were  joined  in  series  with  two  variable 
resistances,  R,  at  least  3  ohms,  and  r,  about  0'4  ohm,  the 
tangent  galvanometer  T,  the  arc  A  and  a  battery  of  accumu- 
lators, B.  Between  the  point  of  connection  of  R  and  r  and 
the  negative  main,  a  Dubois  key  K  was  inserted.  Hence,  when 
K  was  open,  the  arc  was  fed  by  the  mains,  but  when  it  was 
closed,  a  current  flowed  through  the  arc  from  the  accumulators 


82 


THE  ELECTRIC  ARC. 


in    the   direction   opposite   to   that    which    flowed    from    the 
mains. 

The  carbons  used  were  15mm.  in  diameter,  and  both  cored. 
The  arc  was  from  1-5  to  2mm.  in  length. 
The  points  which  Arons  wished  to  determine  were : — 

(1)  What  was  the  least  E.M.F.  in  the  accumulators   with 
which  a  current  could  be  made  to  flow  through  the  hot  vapour 
of   the    arc    immediately   after  it    was    extinguished.      (This 
current  would,  of  course,  with    his  arrangement,  flow   in   the 
reverse  direction,  thus  helping  the  back  E.M.F.  if  there  were 
any  which  continued  after  the  arc  was  extinguished.) 

(2)  What  E.M.F.  was  necessary  in  the  battery  to  enable  it 
to  maintain  an  arc  in  the  reverse  direction,  for  even  only  a 
short  time  after  the  original  arc  was  extinguished. 

It  is  evident,  from  the  arrangement,  that  closing  the  key  K 
both  stopped  the  current  from  the  mains  (and  therefore 
extinguished  the  arc)  and  turned  on  the  reverse  current  from 
the  accumulators.  Hence  no  time  was  lost  between  the  two 
operations. 


MAINS 


FIG.  24. 


As  regards  his  first  point,  Arons  concluded  that  with  the 
carbons  he  employed  the  smallest  E.M.F.  of  the  accumulators 
that  would  send  a  reverse  current  through  the  arc  immediately 
after  it  was  extinguished  was  18  volts.  He  attributed  the  fact 
of  Stenger's  having  been  able  to  send  such  a  current  with  an 
E.M.F.  of  10  volts  to  his  having  used  different  carbons.  He 
considered,  therefore,  that  both  his  and  Stenger's  experiments 
showed  that  the  condition  of  the  carbon  electrodes  and  the 
vapour  after  the  extinction  of  the  arc  was  of  such  a  nature 
that  it  required  a  definite  outside  E.M.F.  to  send  a  current 
through  the  gaseous  space. 

Regarding  the  second  point,  Arons  found  that  the  accumu- 


A  SHORT  HISTORY  OF  THE  ARC.  83 

lators  could  produce  an  arc  in  the  reverse  direction,  after  the 
extinction  of  the  original  arc,  with  a  very  small  P.D.  at  the 
first  moment,  but  that  the  P.D.  necessary  to  maintain  this  arc 
then  rose  rapidly  till  it  reached  its  normal  value.  This,  he 
thought,  was  because  the  E.M.F.  of  the  accumulators  was 
assisted  at  the  first  moment  by  the  still  active  back  E.M.F.  of 
the  original  arc,  which,  however,  very  rapidly  died  away. 
From  his  experiments  he  calculated  this  back  E.M.F.  to  be 
from  10  to  14  volts.104 

Some  experiments  made  in  1896  by  Mr.  W.  E.  Wilson  and 
Prof.  G.  F.  Fitzgerald,  "to  determine,  if  possible,  whether  the 
temperature  of  the  crater  in  the  positive  carbon  varies  when  the 
pressure  in  the  surrounding  gas  is  changed,"  led  to  the  conclu- 
sion that  there  was  not  sufficient  evidence  to  affirm  that  the  tem- 
perature of  the  crater  was  either  raised  or  lowered  by  pressure. 

The  experimenters  first  used  compressed  air,  and  found  that 
with  any  pressure  greater  than  that  of  the  atmosphere,  some  of 
the  radiation  was  cut  off  by  the  formation  of  red  fumes  of  N02, 
which  became  very  plentiful  when  the  pressure  was  as  great  as 
lOOlb.  per  square  inch.  In  compressed  oxygen  the  arc  burnt 
very  steadily,  but  there  was  sufficient  nitrogen  present  in  the 
oxygen  for  enormous  quantities  of  N02  to  be  formed  at  high 
pressures. 

These  results  caused  the  experimenters  to  conclude  that  the 
red  hot  appearance  of  the  crater  and  the  reduction  of  radiation 
in  their  former  experiments  (see  p.  72),  were  due  to  the  forma- 
tion of  large  quantities  of  N02  when  the  arc  was  under  pressure. 

In  hydrogen  contaminated  with  hydrocarbons,  at  atmospheric 
pressure,  the  arc  burnt  very  far  along  both  carbons,  especially 
the  negative.  Trees  of  soot  and  a  deposit  of  hard  graphitic 
carbon  formed  all  round  the  crater,  as  if  there  were  electrolysis 
of  the  hydrocarbon,  and  carbon  were  electro-negative  compared 
with  hydrogen.  The  arc  was  very  unsteady,  both  current  and 
P  D.  varying  continually,  and  the  soot  trees  hid  the  crater,  so 
that  the  attempt  to  get  any  measures  of  radiation  under 
pressure  with  hydrogen  was  abandoned. 

Finally,  carbon  dioxide  was  tried,  a  cylinder  of  C02  being 
connected  with  the  arc  box.  At  pressures  above  1501b.  the  arc 
could  not  be  maintained  long  enough  for  radiation  measures  to 
be  obtained,  but  at  lower  pressures  some  good  measurements 

o2 


84  THE  ELECTRIC  ARG. 

were  made.  With  from  1  to  6  or  7  atmospheres  very  little 
change  of  radiation  appeared  to  take  place. 

Messrs.  Wilson  and  Fitzgerald  consider  that  the  results  of 
their  experiments  render  it  very  improbable  that  it  is  the 
boiling  point  of  carbon  that  determines  the  temperature  of  the 
crater,  and  this  opinion  is  strengthened  by  the  fact  that  the 
carbon  is  so  slowly  evaporated.  "The  crater  of  mercury"  they 
say,  "  is  dark,  but  then  it  volatilises  with  immense  rapidiry,  and 
the  supply  of  energy  by  the  current  being  more  than  100  times 
that  required  merely  for  evaporation,  there  seems  very  little 
reason  why  even  a  considerable  difference  in  latent  heat  should 
make  any  sensible  difference  in  the  rate  of  evaporation  of 
mercury  and  carbon,  especially  as,  at  the  same  temperature, 
the  diffusion  of  carbon  vapour  is  nearly  three  times  as  fast 
as  that  of  mercury  vapour,  and  the  temperature  immensely 
higher."105 

M.  Guillaume,  in  a  Paper  read  before  the  French  Physical 
Society,  said  that  he  believed  the  reduction  of  brilliancy  found 
by  Mr.  Wilson  in  his  experiments  on  the  arc  under  pressure 
(see  p.  72)  was  due  to  carbon  being  dissolved  in  the  sur- 
rounding atmosphere.  He  considered  his  theory  was  proved  by 
the  fact  of  Messrs.  Wilson  and  Fitzgerald  having  found  in  their 
later  experiments  above  that,  with  an  arc  burning  in  C02  at 
a  pressure  of  1501b.,  a  fog  formed  when  the  pressure  was- 
suddenly  reduced.106 

The  much  vexed  question  of  a  back  E.M.F.  in  the  arc  was 
attacked  by  Herzfeld,  who,  like  Stenger  and  unlike  Arons, 
came  to  the  conclusion  that  it  did  not  exist.  He  used  modifi- 
cations of  Edlund's  method  ;  extinguishing  the  arc,  and 
switching  into  the  circuit  immediately  after,  some  instrument 
for  measuring  the  PJ).  between  the  carbons.  In  his  final 
experiment  the  time  that  elapsed  between  the  two  operations 
was  only  -g-i^sec.,  yet  he  could  detect  no  P.D.  between  the 
carbons  even  so  short  a  time  after  the  arc  had  been  extinguished. 

His  next  experiment  was  made  to  determine  whether  the 
P.D.  between  the  carbons  depended  in  any  way  on  the  amount 
of  carbon  transferred  from  one  pole  to  the  other.  The  arc  was 
placed  between  two  plates  6cm.  high  and  8cm.  broad,  the 
distance  between  them  being  varied  from  2cm.  to  10cm.  The 
P.D.  between  them  was  1,800  volts.  The  plates  could  be 


A  SHOUT  HISTORY  OF  THE  ARC. 


85 


connected  with  a  Leyden  jar,  and  either  both  insulated,  or  one 
insulated  and  the  other,  with  the  part  of  the  Leyden  jar  to 
which  it  was  attached,  earthed.  As  it  was  found  that  the 
ultra-violet  rays  of  the  arc  quickly  discharged  the  condenser, 
the  charge  was  kept  up  by  means  of  a  Holz  machine. 

It  was  found  that  although,  when  the  electric  field  was 
excited,  the  particles  sent  out  from  the  positive  towards  the 
negative  carbon  were  continually  attracted  to  the  insulated  plate, 
yet  that  neither  the  current  nor  the  P.D.  between  the  carbons 
was  changed  within  the  limits  of  sensibility  of  a  Schuckert's 
ammeter  and  voltmeter  by  this  withdrawal  of  carbon  particles 
from  the  arc. 

The  particles  were  always  attracted  to  the  insulated  plate 
and  arranged  themselves  radially  on  it  (Fig.  25)  whether  it 


To  the 
Ley  Jen  Jar. 


i  To  Earth. 


FIG.  25. 


was  charged  positively  or  negatively,  even  when  it  was  8cm. 
from  the  carbons,  while  the  earthed  plate  was  only  O'Gcm. 
from  them.  If  both  plates  were  insulated  the  particles  went 
to  both  equally.  Herzfeld  thought  that  perhaps  the  narrow 
double  ring  of  particles  that  ranged  themselves  below  the 
radial  lines  (Fig.  25)  were  those  sent  out  from  the  negative  to 
the  positive  carbon.  The  flow  of  particles  could  be  plainly  seen 
in  an  image  of  the  arc  projected  through  a  lens. 

The  author  considered  that  his  experiment  showed  that  the 
supposed  back  E.M.F.  in  the  arc  cannot  be  due  to  a  polarisa- 
tion of  the  electrodes  taking  place  through  separated  solid 
particles,  since  the  P.D.  did  not  vary  with  the  number  of  solid 
particles  that  really  reached  the  one  electrode  from  the  other. 


86  THE  ELEGT11IC  AEG. 

To  see  if  a  polarisation  took  place  through  the  gaseous 
portion  of  the  arc,  and  if,  therefore,  the  vapour  of  the  arc  was 
affected  by  the  electric  field,  an  enlarged  image  of  the  arc  was 
made  through  a  spectroscope,  the  slit  of  which  was  perpen- 
dicular or  parallel  to  the  electric  lines  of  force,  but  no  change 
could  be  detected  when  the  electric  field  was  excited. 

Next,  it  was  sought  to  discover  the  cause  of  the  formation 
of  a  mushroom  with  hissing  arcs,  and  of  the  growth  of  the 
negative  carbon  that  takes  place,  even  with  silent  arcs,  under 
certain  circumstances.  It  was  shown,  in  the  following  way, 
that  an  absence  of  sufficient  oxygen  to  burn  the  carbon  will 
cause  these  growths.  The  carbons  were  enclosed  in  glass 
tubes  18mm.  in  diameter,  to  which  the  access  of  fresh  air  was 
restricted  by  a  cork  in  one  end  of  each.  The  carbon  particles 
thus  flew  unburnt  from  the  positive  crater  to  the  negative 
point  and  rested  there.  Thus  the  length  of  the  arc  remained 
unchanged  for  from  five  to  ten  minutes,  the  crater  becoming 
deeper  and  the  point  of  the  negative  carbon  becoming  longer 
all  the  time.  The  growth  on  the  negative  was  in  the  shape 
of  a  corkscrew. 

To  test  whether  this  form  was  due  to  magnetic  forces 
induced  by  the  regulating  magnet  in  the  base  of  the  lamp,  the 
negative  carbon  was  surrounded  by  an  electromagnet  to  within 
5cm.  of  its  point,  and  it  was  found  that  changing  the  polarity 
of  this  magnet  changed  the  direction  of  the  corkscrew,  which 
was  from  1-2  to  2mm.  in  height,  while  the  maximum  number 
of  screw  turns  was  2J.  If  the  spirals  were  formed  from 
positively  electrified  particles  on  their  way  from  the  posi- 
tive to  the  negative  carbon,  then  those  particles  moved  in 
the  opposite  direction  from  Ampere's  molecular  streams  of 
electromagnets. 

To  try  what  effect  cooling  each  carbon  and  the  arc  itself 
separately  had  on  the  P.D.  between  the  carbons,  Herzfeld 
directed  a  thin  jet  of  carbonic  acid  gas  against  each  in  turn, 
using  7mm.  cored  carbons  placed  in  a  Dubosq  lamp  from  which 
the  regulating  mechanism  had  been  removed.  He  found  that 
whether  the  positive  carbon  was  above  and  the  negative  below, 
or  vice  versa,  or  if  the  arc  was  horizontal ;  whether  the  stream 
was  directed  against  the  positive  or  the  negative  carbon,  in  all 
cases  the  P.D.  between  the  carbons  increased  when  the  cooling 


A  SHORT  HISTORY  OF  THE  ARC.  87 

jet  was  applied,  and,  although  it  diminished  after  the  cooling 
was  discontinued,  it  remained,  in  most  cases,  above  its  normal 
value.  At  the  same  time  that  the  P.D.  increased,  the  current 
in  all  cases  diminished,  under  the  cooling  action  of  the  carbonic 
acid. 

When  the  carbons  were  surrounded  by  an  atmospaere  of 
carbonic  acid  gas  by  being  enclosed  in  a  glass  tube  closed 
beneath  and  filled  with  the  gas,  it  was  found  that  directing  a 
stream  of  the  same  gas  against  either  carbon  increased  the 
P.D.  between  the  carbons  much  less  than  when  they  were  in 
air,  unenclosed. 

A  current  of  air  from  a  foot-bellows  directed  against  either 
of  the  carbons  produced  no  effect  on  the  P.D.  between  them 
when  the  arc  was  burning  silently. 

Herzfeld  considered  that  the  effect  of  the  carbonic  acid  was 
two-fold ;  it  both  cooled  the  tips  of  the  carbons,  and  increased 
the  resistance  of  the  arc  itself  by  lowering  its  temperature. 
That  the  effect  was  not  thermo-electric  was,  he  thought,  proved 
by  the  following  experiment.  A  rod  of  graphite  1mm.  thick 
was  placed  in  the  arc  midway  between  the  two  carbons,  and 
the  P.D.  between  the  graphite  and  each  of  the  carbons  was 
measured  with  a  d'Arsonval  galvanometer  with  170,000  ohms  in 
circuit.  The  P.D.  of  about  85  volts  between  the  positive 
carbon  and  the  graphite  was  increased  by  2'1  volts  when  the 
positive  carbon  was  cooled  by  the  carbonic  acid,  and  the  P.D. 
of  6  volts  between  the  graphite  and  the  negative  carbon  was 
also  increased  by  2 '8  volts  when  the  latter  was  cooled  in  the 
same  way. 

In  his  concluding  experiments  Herzfeld  made  a  comparison 
between  open  arcs  and  those  enclosed  in  glass  tubes,  the 
E.M.F.  of  the  accumulators  being  constant,  and  the  arc  being 
allowed  to  burn  away  unregulated  till  it  went  out.  The 
following  results  were  obtained  : — 

(1)  The  time  between  the  P.D.  between  the  carbons  attain- 
ing a  given  value  and  the  arc  going   out  was  much  greater 
when  the  arc  was  enclosed. 

(2)  The  P.D.  between  the  carbons  when  the  arc  went  out 
was  greater  when  it  was  enclosed. 

(3)  Greater  lengths  of  the  ends  of  the  carbons  glowed  after 
the  arc  went  out  when  it  was  enclosed. 


88 


THE  ELECTRIC  AUG. 


When  the  enclosing  tube  was  filled  with  carbonic  acid  gas 
the  carbons  burnt  away  very  quickly,  and  after  the  arc  was 
extinguished  a  blue  light  was  frequently  seen,  both  of  which 
facts  appeared  to  the  author  to  show  that  the  carbonic  acid  was 
split  up,  in  higher  temperatures,  into  carbonic  oxide  and  oxygen, 
the  latter  enabling  the  carbons  to  burn  away  more  quickly. 

The  conclusion  arrived  at  by  the  author,  as  the  result  of 
his  experiments,  was  that  the  great  heat  produced  at  the  crater 
is  not  a  Peltier  effect,  but  that  a  substance  of  great  resistance 
is  accumulated  at  the  boundary  between  the  positive  carbon 
and  the  *a?i  which  is  heated  by  the  passage  of  the  current 
through  it,  and  which  vaporises  the  positive  carbon.  This 
vapour,  he  thinks,  condenses  into  fluid  and  solid  drops  in  the 
cooler  parts  of  the  arc.107 

The  same  question  of  the  existence  of  a  back  E.M.F.  in  the 
arc  was  attacked  by  M.  Blondel  in  the  following  manner.  The 
circuit  of  a  continuous  current  arc  was  periodically  interrupted 


FIG.  26. 

at  very  short  intervals  and  for  very  short  periods,  and  during 
each  interruption  the  two  carbons  were  connected  with  a 
galvanometer. 

These  operations  were  carried  out  by  the  revolving  commu- 
tator in  Fig.  26,  which  also  shows  the  circuits  and  general 
arrangements.  The  commutator  T,  driven  by  a  continuous- 
current  constant  speed  motor,  consisted  of  an  ebonite  core 
on  which  there  were  two  copper  rings  b  and  b',  one  of  which 
was  broader  than  the  other.  The  ring  b  had  a  piece  cut 
out  of  it,  and  in  this  indentation  there  was  a  tongue  a 
forming  part  of  the  ring  b'  and  two  copper  insulated  plates  c 


A  SHOBT  HISTORY  OF  THE  ARC.  89 

and  c'.  All  these  parts  were  separated  by  strips  of  mica, 
and  the  brushes  themselves  were  also  insulated  from  their 
holders  by  ebonite,  so  that  the  insulation  resistance  between 
any  two  of  the  brushes  resting  on  the  commutator  and 
between  each  brush  and  earth  always  exceeded  5  megohms. 
This  commutator  revolved  at  a  speed  of  about  40  revolutions  a 
second.  The  piece  cut  out  of  the  ring  b  was  about  one-fifth  of 
the  circumference.  The  arc  lamp  was  fed  by  the  battery  B, 
giving  about  70  volts.  The  current  traversed  successively  the 
steadying  resistance  S,  and  the  commutator  between  M  and  P 
across  the  ring  b,  then  the  lamp  E  F  and  the  switch  C.  At 
every  re  volution  the  circuit  was  broken  during  1/5  x  1/40  =  1/200 
of  a  second  by  the  passage  of  the  indentation  beneath  the 
brush  P,  the  spark  being  taken  on  the  insulated  plate  c. 
These  interruptions  were  very  brief  and  followed  very  close  on 
one  another.  The  arc  was  perfectly  stable,  and  could  not  be 
distinguished  from  an  ordinary  continuous-current  arc. 

The  arc  having  become  steady,  q  and  r  were  connected 
so  that  the  arc  was  short-circuited  by  the  galvanometer  G,  which 
was  fairly  sensitive,  during  the  passage  of  the  tongue  a  under 
the  brush  P  (about  -g^th  of  a  second).  The  author  considered 
that  with  this  arrangement  there  was  no  reason  to  fear  the  in- 
fluence of  cooling  on  the  physical  conditions  of  the  arc  during 
its  extinction,  nor,  consequently,  during  the  passage  of  the 
tongue  a.  If  there  existed,  therefore,  an  E.M.F.  or  ordinary 
polarisation,  it  should  betray  itself,  the  author  thought,  by 
producing  a  permanent  and  easily-observed  deflection  of  the 
galvanometer. 

A  battery,  p,  usually  a  single  cell,  interposed  in  the  galvano- 
meter circuit,  first  one  way  and  then  the  other,  enabled  him  to 
estimate  the  value  of  this  E.M.F.  and  satisfy  himself  as  to  the 
sensitiveness  of  the  method  ;  it  was  only  necessary  to  take  two 
readings  of  the  deflections  obtained  with  the  battery  plus  the 
arc,  and  to  compare  them  with  that  given  by  the  arc  alone. 

Finally,  he  substituted  the  resistance  R,  taking  the  same 
current  at  the  same  voltage,  for  the  arc  itself,  and  then  carried 
out  the  same  series  of  measurements  as  on  the  lamp,  and  was 
thus  able  to  discover  in  what  the  two  phenomena  differed. 

These  experiments  were  carried  out  under  the  most  diverse 
conditions,  with  long  arcs  and  short,  silent  ones  and  whistling, 


90 


THE  ELECTRIC  AEG. 


with  carbons  far  apart  and  sticking  together,  with  solid  car- 
bons S,  or  cored  carbons  C,  and  the  results  presented  no 
other  difference  than  such  as  would  arise  from  experimental 
errors.  The  speed  of  rotation  of  the  commutator  was  also 
varied  within  wide  limits  without  causing  any  appreciable 
difference.  It  was  found,  however,  that  a  speed  of  the  order 
previously  mentioned  or  even  a  higher  one,  was  necessary  in 
order  to  obtain  steady  arcs  and  steady  galvanometer  deflections. 
Table  IX.  is  a  summary  of  a  few  of  the  series  of  figures 
obtained. 

Table  IX.  (Blondel). 


*j 

Arc. 

Resistance. 

*o  S 
o'C 

Nature 
of 

Ter- 

Galv. Deflections 

Ter- 

Galv. Deflections. 

"  P. 

X 

Carbons. 

Amp. 

minal 
Volts. 

Arc 
alone. 

Arc 
plus  cell. 

Amp. 

minal 
Volts. 

Resist, 
alone. 

Resist, 
plus  cell. 

Upper  Lower 

+          _ 

+          _ 

1 

C     S 

5 

35 

7 

70     -78 

5 

34-5 

0 

71-5  -75 

2 

S     S 

8 

25 

1 

75     -72 

8 

27-7 

-9-5 

66     -83 

3 

S     S 

10 

18 

0 

75     -73 

10 

18 

-4 

73     -78 

4 

S     S 

8 

18 

-3-5 

73     -75 

8 

18 

-8 

67     -82 

5 

S     S 

11 

4 

1-3 

80     -73 

11 

4 

0-5 

76     -73 

6 

C     S 

7 

20 

1 

73     -73 

7 

20 

1 

76     -74 

7 

C     S 

7-5 

20 

2 

71     -74 

7-5 

20 

-3 

71     -75 

8 

C     S 

8 

18 

—  5 

70     -7£ 

8 

17-7 

-6 

68     -79 

9 

S     S 

8 

19 

-1 

72-5  -  77 

8-25 

17-5 

1-2 

75-5  -73 

10 

C     S 

6 

29 

2-5 

70     -75 

6 

29 

2-5 

77     -74 

M.  Blondel  pointed  out  that  the  deflections  produced  by  the 
arc  plus  the  cell  of  2 '25  volts  E.M.F.  were  very  large  com- 
pared with  those  produced  by  the  arc  alone.  He  considered 
that  the  above  table  showed  that  if  there  were  a  constant 
counter  E.M.F.  in  the  arc  it  could  not  be  greater  than 

1x2-25  =  0-16  volt. 

M.  Blondel  concluded  from  his  experiments  that,  although 
the  arc  may  not  be  of  the  exact  nature  of  an  ordinary  resis- 
tance, yet  that  it  behaves  sensibly  like  a  resistance,  and  pos- 
sesses no  counter  E.M.F.,  in  the  ordinary  sense  of  the  term, 
comparable  with  the  observed  P.D.  It  is  not  due,  therefore, 
he  thinks,  to  an  electrolytic  phenomenon,  and  if  there  be  a 
residual  E.M.F.  due  to  thermo-electric  causes,  this  cannot 
exceed  a  fraction  of  a  volt.109 


A  SHORT  HISTORY  OF  THE  ARC.  91 

Granquist,  in  criticising  Arons'  latest  experiments  on  the 
back  E.M.F.  of  the  arc  (see  p.  81),  said  that  he  thought  the 
reason  Arons  could  not  apparently  get  a  current  to  flow  in  the 
reverse  direction  through  the  carbons,  immediately  after  the  arc 
was  extinguished,  with  a  less  P.D.  than  18  to  22  volts,  was  that 
the  tangent  galvanometer  he  used  was  not  sensitive  enough  to 
detect  the  current. 

He  pointed  out  that  since  the  dying  out  of  the  vapour 
between  the  carbons  after  the  arc  was  extinguished  was  a 
cooling  effect,  it  was  probable  that  the  time  taken  by  the 
operation  depended  to  some  extent  on  the  amount  of  vapour 
existing  while  the  arc  was  burning,  and  therefore  on  the 
current  flowing  through  the  arc.  The  very  sending  of  a 
current  through  the  carbons  would  tend  to  increase  the  heat 
of  this  vapour,  and  hence  to  retard  the  dying-away  process. 
He  had  himself  found  this  to  be  the  case,  for  he  could  send  a 
current  through  the  arc  for  a  much  longer  time  after  it  was 
extinguished  when  a  large  current  had  been  flowing,  than  when 
there  had  been  a  small  one.  Also,  he  could  send  a  large  current 
in  either  direction  for  a  longer  time  than  a  smaller  one,  after 
the  arc  was  extinguished. 

Granquist  himself  had  found  that  he  could  send  a  current  in 
either  direction  through  the  carbons  immediately  after  the  arc 
was  extinguished,  with  a  single  DanielPs  cell.  The  experi- 
ments were  made  in  1894,  but  as  the  results  were  only 
published  in  Swedish,  he  gave  a  short  account  of  them  in  a 
Paper  published  in  German  in  1897. 

Fig.  27  shows  the  apparatus  used.  D  was  a  Siemens  shunt 
dynamo,  G  an  ammeter,  A  the  arc,  B  a  DanielPs  cell,  M  a 
mercury  contact,  and  B.  a  reversing  switch  by  means  of  which 
the  current  from  B  could  be  reversed  ;  G'  was  a  galvanometer 
constructed  by  Granquist  himself  on  the  principle  of  unipolar 
induction,  which,  as  it  contained  no  coils  of  wire,  might  be 
considered  to  be  free  from  self-induction ;  a,  b  and  c,  were  three 
metal  brushes  which  rubbed  against  the  wheel  W  and  the 
two  wheels  attached  to  it,  each  235 -5mm.  in  circumference,  the 
one  of  ebonite  and  the  other  of  metal.  All  three  wheels 
were  joined  firmly  together,  so  that  they  rotated  on  the  same 
axis.  In  the  periphery  of  the  metal  wheel  a  slot  34mm.  in 
length  was  cut  and  filled  in  with  ebonite.  Similarly,  in  the 


92  THE  ELECTRIC  ARC. 

periphery  of  the  ebonite  wheel  a  slot,  21mm.  in  length,  was 
cut  right  down  to  the  mstal  axis,  and  filled  in  with  brass,  so 
that  when  this  part  of  the  wheel  came  under  the  brush  6  there 
was  electric  connection  between  b  and  the  wheel  W.  The 
wheels  were  so  arranged  that  when  the  brush  a  was  on  the 
ebonite  part  of  the  metal  wheel,  the  brush  b  was  on  the  metal 
part  of  the  ebonite  wheel.  Thus,  when  the  dynamo  circuit 
was  broken,  the  circuit  c  A  M  R  b  was  closed. 

It  was  necessary  that  the  dynamo  circuit  should  be  open 
longer  than  the  galvanometer  circuit  was  closed,  in  order  to 
allow  time  for  the  spark  which  would  pass  at  breaking  to  die 
away,  and  for  the  arc  circuit  to  be  really  completely  broken 
before  the  galvanometer  circuit  was  closed.  Hence,  the  ebonite 
part  of  the  metal  wheel  was  34mm.  in  length,  while  the  metal 


FIG.  27. 

part  of  the  ebonite  wheel  was  only  21mm.  Thus,  the  dynamo 
circuit  was  broken  1'5  times  as  long  as  the  galvanometer 
circuit  was  closed,  so  that  by  moving  the  brush  b,  and  changing 
the  speed  of  rotation  of  the  wheels,  the  time  between  the  open- 
ing of  the  dynamo  circuit  and  the  closing  of  the  galvanometer 
circuit  could  be  altered  at  will. 

The  following  was  the  method  of  experimenting.  After  the 
wheels  had  been  set  in  motion  and  the  carbons  brought  into 
contact,  the  dynamo  circuit  was  closed.  As  soon  as  the  arc 
was  well  established,  the  circuit  of  the  cell  B  was  also  closed 
by  means  of  the  mercury  contact  M.  A  deflection  'U1  was  thus 
obtained  in  the  galvanometer  G'.  The  current  was  then 


A  SHORT  HISTORY  OF  THE  ARC.  93 

reversed  by  means  of  the  switch  E,  and  the  deflection  U2 
observed.  Then,  if  E  were  an  E.M.F.  in  the  arc,  and  the 
E.M.F.  of  the  cell  were  e, 


In  the  following  table  U^  and  U2  were  the  deflections  of  the 
galvanometer,  and  E  the  supposed  back  E.M.F.  of  the  arc. 
The  time  which  elapsed  between  the  complete  breaking  of  the 
current  and  the  closing  of  the  galvanometer  circuit  was  O'OOOO 
second. 

Table  X.  (Granquist.) 


Current  in  arc. 

U,. 

U2. 

E. 

6-2 

+  30-0 

-181 

0-27 

6-2 

24-0 

141 

0-26 

5-0 

22-0 

13-5 

0-26 

5-2 

23-8 

14-5 

0-24 

3-2 

19-7 

11-5 

0-26 

7-5 

20-2 

13-5 

0-20 

5-6 

14-4 

10-0 

0-20 

8-9 

14-5 

17-7 

0-11 

5-0 

20-5 

12-7 

0-23 

40 

17-0 

10-5 

0-24 

mean  0'227  volt. 

Hence  Granquist  found,  as  Lecher,  Luggin,  and  Stenger  had 
already  done,  that  there  was  no  back  E.M.F.  in  the  arc  after 
it  ivas  extinguished  greater  than  about  O227  volt.  Unlike 
Blondel,  however,  he  did  not  think  this  precluded  the  possi- 
bility of  a  far  greater  back  E.M.F.  in  the  arc  ivhile  it  was  burn- 
ing, but  he  considered  that  the  larger  back  E.M.F.  and  the 
current  ceased  to  exist  at  the  same  moment.110 

In  commenting  on  M.  Blondel's  method,  given  above,  of 
proving  that  the  arc  possesses  no  back  E.M.F.  in  the  ordinary 
acceptation  of  the  term,  Prof.  Fleming  suggested  that  there 
might  be  a  back  E.M.F.  due  to  a  "Thomson  effect"  along  the 
hot  vapour  of  the  arc  itself — that  is  to  say,  a  back  E.M.F.  due 
to  the  temperature  gradient  of  the  hot  vapour.  Prof.  Fleming 
mentioned  that  he  and  Prof.  Dewar  had  shown  that  in  carbon 
between  the  temperatures  —  200°  and  +  200°,  the  E.M.F.  caused 
by  the  "Thomson  effect"  acts  from  cool  to  hot  as  it  does  in 
copper.  If  in  carbon  vapour  the  "  Thomson  effect  "  keeps  the 
same  sign  as  in  solid  carbon,  he  thinks  there  might  be  a  back 


34  THE  ELECTEIG  ABC. 

E.M.F.  due  to  it  along  the  column  of  vapour.  This,  he 
said,  would  account  for  the  fact  that  when  the  negative 
carbon  is  heated  the  P.D.  between  the  carbons  for  the  same 
current  is  less  than  when  it  is  unheated,  and  also  for  the 
smaller  P.D.  necessary  for  an  alternating  current  arc,  because 
the  positive  and  negative  carbons  must  be  more  nearly  equal 
in  temperature.111 


CHRONOLOGICAL  LIST  OF  ORIGINAL  COMMUNICATIONS  CONCERNING 

THE  ARC. 

1  Nicholson's  Journal,  4to,  1801,  Vol.  IV.,  p.  326 DAVY. 

2  Gilbert's  Annalen,  1801,  Vol.  VIL,  p.  161          GILBERT. 

3  Gilbert's  Annalen,  1801,  Vol.  VII.,  p.  248          PFAFP. 

4  Gilbert's  Annalen,  1801,  Vol.  VII.,  p.  516          .„         ...  PFAFP. 

5  Gilbert's  Annalen,  1801,  Vol.  VIII.,  p.  370        PFAFF. 

6  Gilbert's  Annalen,  1801,  Vol.  IX.,  p.  341  RITTER. 

7  Nicholson's  Journal,  8vo,  1801,  Vol.  III.,  p.  136  ...  DAVY. 

8  Journal  of  the  Royal  Institution,  1802,  Vol.  I.,  p.  166  ...  DAVY. 

9  Journal  of  the  Royal  Institution,  1802,  Vol.  L,  p.  209  ...  DAVY. 

(  FOURCROY, 

10  Annales  de  Chimie,  An.  IX.  (1801),  Vol.  XXXIX.         ...J  VAUQUELIN, 

(  TH£NARD. 

11  Nicholson's  Journal,  4to,  1802,  Vol.  V.,  p.  238 TROMSDORFF. 

12  Gilbert's  Annalen,  1802,  Vol.  XI.,  p.  396  ,     ANON. 

13  The  Monthly  Magazine,  1803,  Vol.  XV.,  p.  259 PEPYS. 

14  Nicholson's  Journal,  1804,  Vol.  VIII.,  p.  97       CUTHBERTSON. 

is  "  Practical  Electricity  and  Galvanism,"  1807,  p.  260    ....     CDTHBERTSON. 

16  MS.  Note  Book  at  the  Royal  Institution,  1808 DAVY. 

17  Philosophical  Transactions,  1809,  p.  46 DAVY. 

18  MS.  Kote  Book  at  the  Royal  Institution,  1809 DAVY. 

19  The  Monthly  Magazine,  August  1, 1810,  Vol.  XXX. ,  p.  67  DAVY. 

20  "Elements  of  Chemical  Philosophy,"  1812, Vol.  L,  p.  152...  DAVY. 

21  Annales  de  Chimie  et  de  Physique,  1820,  Vol.  XV.,  p.  101  ARAGO. 

22  Philosophical  Transactions,  1821,  p.  18 DAVY. 

23  Silliman's  Journal,  1821,  Vol.  III.,  p.  105  HARE. 

2i  Silliman's  Journal,  1822,  Vol.  V.,  p.  108 ...  SILLIMAN. 

25  Silliman's  Journal,  1823,  Vol.  VI.,  p.  342  ...         ...  SILLIMAN. 

20  Silliman's  Journal,  1826,  Vol.  X.,  p.  123 SILLIMAN. 

27  Philosophical  Magazine,  1838,  p.  436       •         ...  GASSIOT. 

(  GASSIOT, 

28  Iransactions  of  the  London  Electrical  Society,  1837  to  I  WALKER, 

1840,  p.  71        „         ...  1  STURGEON, 


29  Philosophical  Transactions,  1839,  p.  92    ... 

30  Philosophical  Magazine,  1840,  Vol.  XVI.,  p.  478 

31  Comptes  Rendus,  1840,  Vol.  XL,  p.  702     ... 


MASON. 
DANIELL. 
GROVE. 
BECQUEREL. 


A  SHORT  HISTORY  OF  THE  ARC. 


95 


32  Comptes  Rendus,  1841,  Vol.  XII.,  p.  910 

33  Comptes  Rendus,  1841,  Vol.  XIII.,  p.  198 

34  Archives  de  I  Electricity  1841,  p.  575       

35  Poggendorff's  Annalen,  1844,  Vol.  LXIII.,  p.  576 

36  Comptes  Rendus,  1844,  Vol.  XVIIL,  p.  746         

37  Poggendorff's  Annalen,  1845,  Vol.  LXVL,  p.  414 

33  Comptes  Rendus,  1846,  Vol.  XXII.,  p.  690          

39  Comptes  Rendus,  1846,  Vol.  XXIII.,  p.  462         

40  Comptes  Rendus,  1850,  Vol.  XXX.,  p.  201  

41  Comptes  Rendus,  1852,  Vol.  XXXIV.,  p.  805 

42  Philosophical  Transactions,  1852,  p.  88    ...         

43  Comptes  Rendus,  1865,  Vol.,  LX.,  p.  1,002  

44  Poggendorff's  Annalen,  1857,  Vol.  CXXXL,  p.  586.      ... 

45  Poggendorffs  Annalen,  1868,  Vol.  CXXXIIL,  p.  353   ... 

46  Poggendor&s  Annalen,  1868, Vol.  CXXXIV.,pp.  250,  337 

47  Poggendorff's  Annalen,  1870,  Vol.  CXXXIX.,  p.  354    ... 

48  Poggendorff's  Annalen,  1870,  Vol.  CXL.,  p.  552 

49  The  Electrician,  1879,  Vol.  II.,  p.  76        

50  The  Electrician,  Vol.  II.,  1879,  Jan.  18th,  p.  107  ;   and 

25th,  p.  117      

51  Royal    Engineering     Committee    Extracts    for    1879, 

Appendix  III. 
02  La  Lumiere  Electrique,  1879,  Vol.  I.,  p.  41          

53  Philosophical  Transactions,  1879,  p.  159 

54  La  Lumiere  Electrique,  1879,  Vol.  I,  p.  235        

55  Journal  of  the  Society  of  Telegraph  Engineers,   1880, 

Vol.  IX.,  p.  201 

56  La  Lumiere  Electrique,  1881,  Vol.  III.,  p.  220 

57  La  Lumiere  Electrique,  1881,  Vol.  III.,  p.  285 

58  La  Lumiere  Electrique,  1881,  Vol.  III.,  p.  287 

59  Proceedings  Physical  Society,  1882,  Vol.  V.,  p.  X97 

80  Proceedings  of  the  Royal  Society,  1882,  Vol.  XXXIII., 

p.  262 

61  EleUrotechnitche  Zeitschrift,  1883,  Vol.  IV.,  p.  150 

™  Zeitschrift  fur  Elektrotechnik,  1885,  Vol.  III.,  p.  Ill     ... 

63  Wiener  Akad.,  1885,  Vol.  XCL,  §  844      

64  Centralblatt  fur  Electrotechnilc,  1885,  Vol.  VII.,  p.  443... 

65  Wiedemann's  Annalen,  1885,  Vol.  XXV.,  p.  31 

63  Wiedemann's  Annalen,  1885,  Vol.  XXVI.,  p.  518 

67  Proceedings  of  the  American  Academy  of  Sciences, 
1886,  p.  227. 

™  Centralblatt  fur  Elektrotechnilc,  1886,  Vol.  VIII.,  pp. 
517,619  

69  Wiedemann's  Annalen,  1887,  Vol.  XXX.,  p.  93 

70  Wiedemann's  Annalen,  1887,  Vol.  XXXI.,  p.  384 

71  Centralblatt  filr  Elelctrotechnik,  1887,  Vol.  IX.,  p.  219  ... 

72  Centralblatt  fur  EleUrotechnilc,  1887,  Vol.  IX.,  p.  633  ... 


DE  LA  RIVE. 

BECQUEREL. 

MACKRELL. 

CASSELMANN. 
f  FIZEAU, 
\  FOUCAULT. 

NEEF. 

DE  LA  RIVE. 

VAN  BREDA. 

MATTEUCCI. 

QUET. 

GROVE. 

DE  LA  RIVE. 

EDLUND. 

EDLUND. 

EDLUND. 

EDLUND. 

BEZOLD. 

ATRTON. 

SCHWENDLEB. 


DU  MONCEL. 

/  DE  LA  RUE, 

\  MiJLLER. 

ROSSETTI. 

ANDREWS. 
ROSSETTI. 
LE  Roux. 

NlAUDET. 

/  AYRTON, 
\  PERRY. 

DEWAR. 

FROLICH. 

PEUKERT. 

VON  LANG. 

Vox  LANG. 

STENGER. 

EDLUND. 
f  CROSS, 
(  SHEPARD. 

NEBEL. 
ARONS. 
VON  LANG. 

VOGEL. 
UPrENBORN. 


96 


THE  ELECTRIC  AUG. 


73  BeiUiittcr,  1888,  Vol.,  XII.,  No.  1,  p.  83 

74  CentralUatt  fur  EleJctrotechnik,  1888,  Vol  X.,  p.  3 

75  CentralUatt  filr  Elcktrotechnik,  1888,  Vol.  X.,  p.  48       .., 

76  CentralUatt  fur  Elcktrotechnik,  1888,  Vol.  X.,  p.  102    ... 

77  CentralUatt  fur  Elcktrotechnik,  1888,  Vol.  X.,  p.  567    .., 

78  Centralblattfilr  Elektrotechnik,  1888,  Vol.  X.,  p.  591    .., 

79  CentralUatt  fiir  Elcktrotechnik,  1888,  Vol.  X.,  p.  749     .. 

80  Wien  Sitzungsberichte,  1889,  Vol.  XCVIII.,  p.  1,192      .. 
M" Proceedings  of  the  Royal  Society,  1889,  Vol.  XLVIL, 

p.  118 


81  The  Electrical  World,  1891,  Vol.  XVII.,  p.  166 
8-  La  Lumiere  tilcctrique,  1891,  Vol.  XLIL,  p.  621 

83  The  Electrical  World,  1892,  Vol.  XIX.,  p.  195 

*4  The  Electrical  World,  1892,  Vol.  XX..  p.  227     

85  The  Electrician,  1892,  Vol.  XXVIII.,  p.  687,  Vol.  XXIX., 

P.  11       

86  Wiedemann's  Annalen,  1892,  Vol.  XLV.,  p.  33 

87  The  Electrician,  Vol.  XXIX.,  1892,  p.  460          

88  Comptes  Rendus,  1892,  Vol.  CXV.,  p.  1,273        

39  Journal  de  Physique,  1893,  Vol.  II.,  p.  545         


UPPENBORN, 

FEUSSNER. 

LECHER. 

UPPENBORN. 

LUGGIN. 

SCKREIHAGE. 

DTTBS. 

LUGGIN. 

FLEMING. 
f  ELIHU  THOM« 

\  SON. 

BLONDEL. 
CRAVATH. 
CRAVATH. 


'•»  Electrical  Engineer  of  New  York,  1893,  p.  90 


...     TROTTER. 
...     STENGER. 
...    S.P.THOMPSON 
...     VIOLLE. 
...     VIOLLE. 
f  DUNCAN, 
...-!  ROWLAND  and 

(  TODD. 

91  The  Electrician,  1893,  Vol.  XXXIL,  pp.  117,  145,  169  ...     BLONDEL. 

92  Comptes  Rendus,  1894,  Vol.  CXIX.,  p.  949          VIOLLE. 

9:j  The  Electrician,  1894,  Vol.  XXXIII.,  p.  297       TROTTER. 

94  "  Electric  Lamps  and  Electric  Lighting,"  p.  153  ...     FLEMING. 

95  Memoirs  and  Proc.  of  the  Manchester  Lit.  and  Phil.  Soc., 

1895,  Vol.  IX.,  Series  IV.,  p.  139      FRITH. 

9(i  Wiedemann's  Annalen,  1895,  Vol.  LV,  p.  361 LEHMANN. 

97  Proc.  Roy.  Soc.,  1895,  Vol.  LVIIL,  p.  174          WILSON. 

1)8  BeiUdtter,  1895,  Vol.  XIX,  p.  97 GRANQUIST, 

99  The  Electrical  Review,  1895,  Vol.  XXXVII. ,  pp.  230.253,301  FREEDM  AN. 

100  The  Electrical  World,  1895,  Vol.  XXV.,  p.  277 MARKS. 

101  The  Electrical  Engineer  of  New  York,  1895,  Vol.  XIX., 

p.  198 MARKS. 

™  TJie  Electrical  World,  1896,  Vol.  XXVII.,  pp.  262,  378J 

103  The  Philosophical  Magazine,  1896,  p.  407 

IM  Wiedemann's  Annalen,  1896,  Vol.  LVII.,  p.  185 

105  Proceedings  of  the  Royal  Society,  1897,  Vol.  LX.,  p.377-1  WILSON, 

(  FITZGERALD. 

106  The  Electrician,  1897,  Vol.  XXXVIII.,  p.  642 

107  Wiedemann's  Annalen,  1897,  Vol.  LXIL,  p.  435 

*08  L'Adairage  tilcctrique,  1897,  Vol.  X.,  pp.  289,  496,  539 
'°9  The  Electrician,  1897,  Vol.  XXXIX.,  p.  615       

110  Ofversigt  af  Kongl.  Vetenskaps-Akademiens  Forhand- 

lingar,  1897.     N  :  o  8,  Stockholm,  p.  451 

111  The  Electrician,  1898,  Vol.  XL.,  p.  363 


f  FRITH, 


RODGERS. 
ARONS. 


GUILLEAUME. 

HERZFELD. 

BLONDEL. 

BLONDEL. 

GRANQUIST. 
FLEMING. 


CHAPTER  III. 


PHENOMENA   CONNECTED   WITH   THE    "STRIKING"  OF   THE  ARC 
AND  WITH  SUDDEN  VARIATIONS  OF  CURRENT. 

AT  the  Electrical  Congress  held  in  Chicago  in  August,  1893, 
Prof.  Ayrton  read  a  long  Paper  on  the  subject  of  the  Electric 
A™,  which  gave  the  results  of  experiments  that  he  had  been 
carrying  out  with  his  students  during  the  three  preceding 
years.  Neither  the  Paper,  nor  any  abstract  of  it,  was  published 
in  the  report  of  the  Congress,  for  while  it  was  in  the  hands  of 
the  secretary  of  Section  B  of  the  Congress,  it  was  unfortunately 
burnt  five  months  after  it  had  been  read. 

The  experiments  to  which  Prof.  Ayrton  specially  directed 
his  attention  were  briefly  : — 

1.  Obtaining  the  time  variations,  after  striking  the  arc,  of 
the  P.D.  between  the  carbons,  with  various  constant  currents, 
various  constant  lengths   of  arc,    and   with   the  ends  of  the 
carbons  variously  shaped. 

2.  Obtaining  the  time  variation  of   the   P.D.  between  the 
carbons  when  the  current   was   suddenly  changed,    and   the 
length  of  the  arc  was  kept  constant. 

3.  Obtaining  curves  connecting  the  steady  final  values  of  the 
P.D.   between  the  carbons    with   the  current,    for    different 
currents,   lengths    of   arc,    and    sizes  of   carbons,    cored    and 
uncored. 

4.  The  influence  of  varying  the  current  and  the  length  of 
the  arc  on  the  depth  and  width  of  the  crater. 

5.  The  distribution  of  potential  throughout  the  arc. 

6.  The  candle-power  and  efficiency  of  the  arc.  with  various 
currents,  P.Ds.,  and  lengths  of  arc. 


98 


THE  ELECTEIC  ARC. 


The  lamp  used  in  these  experiments   (Fig.  28)  was  hand- 
regulated,  the  adjustments  being  effected  by  turning  pinion  PT 


JTL 


^N^<SSNS>v^^W^x^^ 

FIG.  28.—"  Hand-fed  "  Arc  Lamp. 

to  alter  the  height  of  the  positive  carbon,  pinion  P2  to  alter 
the  height  of  the   negative   carbon,  and   pinion   P3   to  raise 


P.D.  AFTER  "STRIKING"  THE  ARC. 


99 


both  carbons  together.  By  turning  the  nut  Nj  the  positive 
carbon  could  be  turned  about  a  horizontal  axis  in  the  plane  of 
the  figure,  and  by  turning  the  nut  N2  the  positive  carbon  was 
moved  round  a  horizontal  axis  at  right  angles  to  the  plane  of 
the  figure.  To  measure  the  P.D.  between  the  tips  of  the 
carbons,  the  voltmeter  was  attached  to  two  thin  carbon  rods 
kk,  sliding  in  tubes  in  a  block  of  asbestos,  A,  and  pushed 
against  the  main  carbon  rods  C  C  by  spiral  springs  S  S.  Had 
the  P.D.  been  measured  between  the  lamp  terminals,  a 
variable  error  would  have  been  introduced,  from  the  drop  of 
pressure  in  the  carbons  themselves,  which  would  have 
been  serious  with  large  currents  and  long  carbons.  Since 
the  voltmeter  had  a  resistance  of  about  80,000  ohms  in  circuit 


Box  Light  Tight. 


Red  Glass  for 
Examining  Arc. 


^Diagram 
,  Screen.. -- 


FIG.  29.— Plan  of  Arc  Lamp,  Lens,  Mirror  and  Diagram  Screen. 

with  it,  the  resistance  between  the  ends  of  these  auxiliary 
voltmeter  carbons  kk  and  the  main  carbons  CC  introduced 
no  practical  error. 

The  length  of  the  arc  was  always  taken  to  be  the  vertical 
distance  between  the  point  of  the  negative  carbon  and  the  hori- 
zontal plane  drawn  through  the  edge  of  the  crater  of  the 
positive  carbon.  Length  of  arc  "0  millimetres"  does  not, 
therefore,  mean  that  the  carbons  were  in  contact,  but  that  the 
point  of  the  negative  carbon  was  just  entering  the  crater 
at  the  end  of  the  positive  carbon.  This  distance  was  measured 
on  an  image  formed  on  the  diagram  screen,  as  shown  in  Fig.  29 
by  the  lens  L  and  the  plane  mirror  M.  This  image  of  the  arc 
was  exactly  ten  times  full  size. 

H2 


100  THE  ELECTRIC  AEC. 

When  these  experiments  were  first  started,  at  the  beginning 
of  1890,  it  was  not  known  what  were  the  conditions  necessary 
for  the  P.D.  between  the  carbons  to  remain  constant  when  the 
current  and  length  of  arc  were  both  kept  constant,  and  con- 
sequently it  was  found,  as  had  been  found  by  all  previous  ex- 
perimenters, that  a  given  current  could  be  sent  through  an  arc 
of  given  length  by  many  different  potential  differences,  and  that 
no  set  of  experiments  made  one  day  could  be  repeated  the  next. 

In  the  earlier  experiments  a  reading  was  taken  soon  after  the 
current  had  been  brought  to  the  desired  value;  hence  the 
curves  connecting  P.D.  with  current  for  a  constant  length  of  arc 
were  different  for  each  set  of  experiments,  and  were  always 
too  steep.  For  example,  with  both  positive  and  negative 
carbons  cored,  and  both  13mm.  in  diameter,  the  early  curves 
show  that  when  the  arc  had  a  constant  length  of  5mm.  the 
P.D.  fell  from  59  volts  for  a  current  of  4  amperes  to  24  volts 
for  a  current  of  30  amperes;  that  is,  it  was  diminished  by  35 
volts.  Whereas,  in  the  later  experiments,  with  a  13mm.  cored 
positive  carbon  and  an  llmm.  solid  negative,  the  P.D.  fell 
from  GO'S  to  4S'S  volts,  or  only  11 '7  volts  for  the  same  change 
in  current  with  the  same  length  of  arc. 

The  first  step  in  advance  was  made  by  keeping  each  new 
current  flowing  for  a  certain  minimum  time  before  taking  the 
observations.  This  resulted  in  making  the  curves  connecting 
P.D.  with  current  for  a  given  length  of  arc  much  flatter, 
and  not  quite  so  widely  different  with  different  sets  of  experi- 
ments; but  it  was  still  found  that  the  curves  for  values  of 
current  ascending  and  those  for  values  of  current  descending 
were  different. 

Fig.  30  gives  one  of  the  sets  of  curves  drawn  during  this  series 
of  experiments  made  in  1890,  when  it  had  been  found  that 
allowing  a  certain  time  to  elapse  before  the  reading  was  taken 
after  the  current  had  been  altered  made  the  readings  for 
ascending  and  descending  current  more  nearly  equal,  and  also 
made  the  curve  connecting  P.D.  with  current  for  a  given 
length  of  arc  less  steep.  It  was  also  found  that,  if  the  whole 
series  of  readings  could  be  taken  without  the  arc  going  out, 
better  results  were  obtained ;  therefore,  during  the  five  hours 
occupied  by  the  experiments  from  which  Fig.  30  was  taken  the 
arc  was  never  extinguished. 


P.D.  AFTER  "STRIKING  "  THE  ARC. 


101 


A  large  number  of  experiments  were  now  carried  out,  each 
of  which  occupied  the  greater  part  of  a  day,  as  the  current, 
which  was  made  to  slowly  vary  backwards  and  forwards  between 
two  limits,  was  never  stopped,  nor  the  arc  allowed  to  go  out,  for 
many  hours  at  a  time. 

However,  even  with  all  these  precautions,  looped  curves 
similar  to  those  in  Fig.  30  were  obtained,  and  it  is  apparent 
from  these  curves  that  the  P.D.  needed  to  send  a  given  current 
through  the  arc,  which  was  kept  at  a  constant  length  of 
4mm.,  was  never  twice  the  same.  For  instance,  a  cur- 
rent of  10  amperes  (Fig.  30)  was  sent  through  the  arc  by 


40 


10  15  20 

Current  in  Amperes. 


FIG.  30. — 18mm.  cored  carbons.     Arc  not  allowed  to  go  out  during  the 
b  hours'   run.     Termination  of  experiment  due   to  wasting   of  carbons. 

Arc    at    a    constant  length  of   4mm.       Current    increasing, ?- 

Current     decreasing,     ^ Latter    half    of    curve   6   is    dotted 

owing  to  the  length  of  arc  being  indeterminate.  This  was  due  to  ine- 
quality in  the  carbons. 

P.Da.  of  51,  49-5,  49,  48,  46-5,  46-2,  and  46  volts  respectively, 
so  that  for  this  one  current  the  P.Ds.  ranged  from  46  to 
51  volts.  Hence,  from  these  curves  it  would  be  impossible  to 
find  any  exact  relation  between  P.D.  and  current  for  a  given 
length  of  arc. 


102  THE  ELECTRIC  ARC. 

Consequently,  when  the  work  was  taken  up  again,  it  was 
thought  advisable  to  make  a  complete  investigation  of  the 
variation  of  P.D.  with  the  time  that  elapsed  after  the  arc 
had  been  started  or  the  current  suddenly  changed,  the  current 
and  length  of  arc  subsequently  being  kept  constant  during  each 
experiment. 

The  questions  to  which  answers  were  sought  were  the  follow- 
ing :— 

(1)  Does    the    P.D.    ever  become  a   constant   for   a   given 
current  and  length  of  arc  ? 

(2)  If  there  is  a  final  constant  P.D.  for  each  current  and 
length  of  arc,  is  this  P.D.  the  same,  and  is  the  time  taken  to 
reach  it    after  starting   the   same,    whether   a   cored    or   an 
uncored  positive  carbon  is  used  ? 

(3)  What  are  the  causes  of  this  variation  of  P.D.  ? 

(4)  How  is  the  time  before  this  P.D.  is  reached  affected  by 
the  employment  of  (a)  different  lengths  of  arc,  (b)  different 
currents  ? 

(5)  How  is  this  period  of  time  affected  by  the  current  that 
was  flowing  through  the  arc  before  the  change  was  made  ? 

The  experiments  from  which  Figs.  31  to  35  were  taken 
answered  the  first  three  questions.  They  showed  that  the 
P.D.  does  reach  a  final  constant  and  steady  value,  that  coring 
the  positive  carbon  increases  the  period  of  time  which  elapses 
after  starting  the  arc  before  the  final  value  of  the  P.D.  is 
reached,  and  they  showed  the  causes  to  which  the  variation 
of  the  P.D.  is  due. 

These  experiments  were  all  made  with  positive  carbons 
18mm.  and  negative  carbons  15mm.  in  diameter.  The  positive 
carbon  was  in  some  cases  cored  as  is  indicated  in  the  figures, 
and  in  other  cases  solid,  and  the  negative  carbons  were  solid  in 
all  cases.  Also  the  current  used  was  10  amperes,  and  the 
length  of  the  arc  was  3mm.  for  all  the  experiments  except 
those  which  answered  question  (4).  The  first  point  on  each  of 
the  curves  was  taken  the  moment  the  carbons  had  been 
separated  to  a  distance  of  3mm.  after  striking  the  arc. 

It  is  evident  that  question  (1)  is  answered  in  the  affirma- 
tive, for  after  a  shorter  or  longer  time  the  P.D.  in  all  cases 
finally  reached  a  constant  steady  value  of  from  44  to  46  volts,. 
when  the  positive  carbon  was  cored,  and  from  47  to  50  volt& 


P. I).  AFTER  "STRIKING"  THE  ARC. 


103 


when  it  was  solid  (Figs.  31  to  35),  the  slight  variation  of 
P.D.  finally  arrived  at  with  the  same  current  and  length  of  arc 
for  the  same  kind  of  carbons  being  accounted  for  by  the  fact 
that  every  pair  of  carbons  differs  slightly  from  every  other 
pair  in  hardness  and  structure. 


65 


50 


45 


40 


35 


25 


20 


10  20  30 

Time  in  Minutes. 


40 


60 


FIG.  31.-  -Current  suddenly  started  and  maintained  at  10  amperes. 
Length  of  arc  maintained  at  3mm.  Carbons  :  Positive,  18mm.  cored  ; 
negative,  15mm.  solid.  The  positive  carbon  was  shaped  as  it  came  from 


the  makers,  thus,  shown  full  size.     The  negative  was  shaped  by  being  pre- 
viously used  in  a  3mm.  arc  with  a  current  of  10  amperes. 


104  THE  ELECTRIC  AEC. 

Fig.  31  shows  the  connection  between  P.D.  and  time  after 
starting  the  arc,  when  the  positive  carbon  is  cored  and  shaped 
as  it  came  from  the  maker,  and  the  negative  has  previously 
been  used  with  a  current  of  10  amperes  and  an  arc  of  3mm. 
till  the  P.D.  has  become  constant.  To  save  using  this 
expression  again  and  again,  I  shall  call  a  carbon  'normal'  when 
it  has  been  burnt  long  enough,  with  a  given  current  and  an 
arc  of  given  length,  for  the  P.D.  to  have  reached  its  steady 
value,  and  I  shall  call  an  arc  *  normal '  when  it  is  burning 
with  '  normal '  carbons. 

It  will  be  observed  in  Fig.  31  that  after  the  length  of  the 
arc  had  been  adjusted  at  3mm.  the  P.D.  between  the  carbons 
fell  to  the  low  value  of  16  volts.  Hence  a  genuine  arc  3mm.  in 
length  can  be  maintained  silently,  at  any  rate  for  a  short  time, 
with  a  P.D.  of  only  16  volts.  It  was  thought  probable 
that  this  very  low  P.D.  might  have  been  caused  in  some 
way  by  the  soft  core  of  the  positive  carbon,  and  experi- 
ments were,  therefore,  made  with  cored  and  uncored  positive 
carbons  under  precisely  similar  conditions.  The  tips  of  the 
positive  carbons  were  filed  flat,  and  they  were  used  with 
negatives  that  were  'normal'  for  10  amperes  and  3  millimetres. 

The  results  may  be  seen  in  Fig.  32,  curves  A  A  A  and  B  B  B. 
Curve  A  A  A,  which  was  obtained  with  a  solid  positive  carbon, 
starts  with  a  P.D.  of  44  volts,  while  BBB,  for  which  the 
positive  carbon  was  cored,  starts  with  one  of  25  volts.  The 
low  P.D.  at  starting  is,  then,  caused  by  the  positive  carbon 
being  cored.  But  why  should  there  be  such  a  great  difference, 
namely,  19  volts,  in  the  P.Ds.  at  starting,  when  the  difference 
between  the  steady  values  of  the  P.Ds.  is  only  about  four  volts  ? 

To  settle  this  question  an  arc  was  started  with  a  cored  posi- 
tive carbon  shaped  as  when  it  came  from  the  makers,  and  a 
'  normal '  negative,  and,  after  burning  for  less  than  one  second, 
the  current  was  suddenly  turned  off.  On  examining  the  car- 
bons it  was  found  that  the  core  had  been  torn  out  of  the  posi- 
tive carbon  to  the  depth  of  one  eighth  of  an  inch,  while  the 
negative  carbon  was  covered  with  the  finely-powdered  material. 
All  this  extra  loose  and  easily  volatilised  carbon  would,  of  course, 
much  enlarge  the  cross-section  of  the  arc,  and  thus  lower  its  appa- 
rent resistance,  and  also  the  current  probably  flows  with  a  much 
smaller  P.D.  when  it  is  conveyed  by  means  of  small  particles 


P.D.  AFTER  "STRIKING"  THE  ARC. 


105 


of  carbon  actually  travelling  across  the  arc  than  when  it  flows 
simply  through  volatilised  carbon.  For  this  reason,  it  is  pro- 
bable that  the  fact  that  particles  of  unvolatilised  carbon  fall  in 
showers  from  the  positive  carbon  when  there  is  hissing  partly 
accounts  for  the  fall  of  P.D.  in  the  arc  in  that  case. 

In  curve  C  C  C  (Fig.  32)  the  crater  of  the  positive  carbon 
had  already  been  formed  mechanically,  and  therefore  the 
P.D.  started  higher  than  in  curve  B  B  B,  and  remained  higher 
for  about  45  minutes;  in  fact,  for  half  an  hour  it  more  nearly 


30  40  50 

Time  in  Minutes. 

FIG.  32. — Current  suddenly  started  and  kept  at  10  amperes.  Length  of 
arc  kept  at  3mm.  Carbons :  Positive,  18mm.  solid  or  cored  ;  negative, 
15mm.  solid.  Negative  carbon  in  each  case  shaped  by  being  previously 
used  for  a  long  time  to  form  an  arc  3mm.  long,  with  a  current  of  10 
amperes.  A  A  A  :  Positive  carbon  solid,  end  filed  flat.  B  B  B  :  Positive 
carbon  cored,  end  filed  flat.  C  C  C  :  Positive  carbon  cored,  with  a  crater 
mechanically  made  at  the  end  after  it  was  filed  flat. 

coincided  with  A  A  A,  the  curve  for  solid  carbons,  than  with 
B  B  B,  which  is  not  to  be  wondered  at,  seeing  that  the  part 
s>f  the  carbon  from  which  the  core  had  been  mechanically 


106  THE  ELECTRIC  ARC. 

extracted,  was  practically  solid ;  and  thus,  while  it  burnt  away, 
there  was  very  little  loose  soft  carbon  to  be  easily  volatilised, 
and  so  lower  the  P.D. 

The  time  that  the  P.D.  takes  to  reach  its  constant  value 
when  the  positive  carbon  is  flat  to  start  with  is  very  remark- 
able. From  Fig.  32  we  see  that  with  a  flat- tipped  positive 
carbon  of  18mm.  diameter  and  a  *  normal '  negative  carbon  of 
15mm.  diameter,  when  a  constant  current  of  10  amperes  was 
flowing  through  an  arc  of  3mm.,  the  P.D.  did  not  acquire  its 
constant  value  till  50  minutes  after  the  arc  ivas  struck  with 
a  solid  positive  carbon,  and  an  hour  after  with  a  cored  positive 
carbon.  How  important  a  fact  this  is  may  be  gathered  from 
the  consideration  that  the  P.D.  which  would  send  a  current 
of  10  amperes  through  an  arc  of  3mm.  when  the  positive 
carbon  was  cored,  might  have  been  put  down  as  being  anything 
from  25  to  48  volts  (curve  B  B  B,  Fig.  32),  according  to  the 
time  that  had  been  allowed  to  elapse  after  striking  the  arc 
before  the  reading  was  taken.  Of  course  such  a  wide  range 
of  P.D.  for  such  a  current  would  only  be  possible  when 
the  positive  carbon  was  cored  and  had  been  flat  before 
striking  the  arc,  but  curve  A  A  A,  Fig.  32,  shows  that 
even  with  a  solid  positive  carbon  the  P.D.  may  range 
from  about  44  to  52  volts.  With  small  currents  of  2  or  3- 
amperes  I  have  found  that  with  both  carbons  solid  the  P.D. 
may  take  as  much  as  two  and  a  half  hours  to  acquire  its 
constant  value,  even  when  the  positive  carbon  has  not  been 
filed  flat,  but  has  been  shaped  beforehand  by  some  such 
current  as  5  or  6  amperes. 

It  is  possible  that  the  extra  low  P.D.  at  starting  in  Fig.  31 
may  have  been  caused  by  the  positive  carbon  with  a  pointed 
tip  being  easier  to  volatilise  than  the  one  with  a  flat  tip. 
The  reason  that  the  P.D.  took  such  a  short  time  to  reach  its 
steady  value — only  five  minutes — must  have  been  that  when  the 
carbon  from  the  crater  had  been  volatilised  it  only  came  in 
contact  with  the  hot  tip,  and  was  not  cooled  down  by  the 
mass  of  comparatively  cold  carbon  surrounding  the  crater,  as 
happened  when  the  tip  was  flat.  This  mass  of  cold  carbon  is 
evidently  the  cause  of  the  P.D.'s  not  retaining  its  constant 
value  when  it  first  reaches  it,  but  rising  to  a  higher  value 
and  then  falling  again,  as  it  does  in  all  the  curves  in  Figs. 


P.D.  AFTER  "STRIKING"  THE  ARC. 


107 


31,  32,  and  33.  For,  from  the  time  of  starting  the  arc,  this  mass 
of  carbon  was  heated  sufficiently  for  it  to  gradually  burn  away, 
therefore  part  of  the  heat  of  the  crater  was  used  in  warming 
up  this  surrounding  carbon  until  it  was  all  burnt  away,  and 
the  positive  carbon  had  become  normal.  This  took  place 
between  50  minutes  and  an  hour  after  the  arc  was  started. 
The  extra  amount  of  heat  needed  during  this  time  meant,  of 
course,  that  a  higher  P.D.  was  required  to  send  the  same 
current  through  the  arc ;  for,  since  the  rate  of  production  of 
heat  depends  upon  the  current  multiplied  by  the  P.D.,  and  the 
current  was  kept  constant,  the  P.D.  was  bound  to  be  higher. 
Hence  the  "  hump,"  which  will  be  found  in  every  curve  for 
which  a  flat  positive  carbon  has  been  used. 


•26 


30  40  50 

Time  in  Minutes. 


FIG.  33.  — Current  suddenly  started  and  kept  at  10  amperes.  Length  of 
arc  kept  at  3mm.  Carbons  : — Positive,  18mm.  solid  ;  negative,  15mm. 
solid.  Negative  carbon  normal  in  each  case.  A  A  A :  End  of  solid 
positive  carbon  filed  flat.  D  D  :  Hole  2in.  deep  drilled  in  end  of 
solid  positive  carbon.  E  E  E  :  Hole  lin.  deep  drilled  in  end  of  solid 
positive  carbon  and  packed  tightly  with  soft  carbon,  end  filed  flat. 

The  curves  in  Fig.  33  are  interesting  as  showing  how 
completely  and  certainly  the  core  of  the  positive  carbon  is 
responsible  for  a  very  low  P,D.  on  starting  the  arc. 


108  THE  ELECTRIC  ARC. 

With  the  curve  E  E  E,  in  which  the  P.D.  started  at 
about  27  volts,  the  positive  carbon  was  solid,  but  drilled 
to  the  depth  of  one  inch,  and  packed  moderately  tightly 
with  the  carbon  from  a  soft  core.  For  the  first  three  minutes, 
therefore,  it  behaved  exactly  as  if  it  were  cored  in  the  usual 
way,  and  after  that  it  acted  like  a  completely  solid  carbon.  It 
is  a  little  curious  that  the  effect  of  a  whole  inch  of  soft  core 
should  apparently  have  exhausted  itself  in  three  minutes,  and 
that  from  that  time  onwards  the  curve  obtained  with  the 
drilled  and  packed  positive  carbon  should  be  almost  identical 
with  that  obtained  with  an  ordinary  solid  positive  carbon  (see 
curve  A  A  A,  Fig.  33).  One  would  have  expected  the  'hump' 
to  be  lower  with  the  drilled  and  packed  positive,  on  account  of 
the  loose  soft  carbon.  Probably,  however,  the  carbon  was  not 
as  tightly  packed  as  in  a  manufactured  core,  and,  therefore, 
most  of  it  was  shot  out  during  the  first  three  minutes  after 
starting  the  arc,  only  enough  of  it  being  left  to  keep  the  posi- 
tive carbon  from  behaving  as  if  it  had  merely  a  hole  and  no 
core  at  all. 

Curve  D  D,  Fig.  33,  shows  what  that  behaviour  would 
have  been.  The  positive  carbon  in  this  case  had  a  hole  two 
inches  deep  drilled  in  it,  and  left  hollow,  and  this  kept  the 
P.D.  slightly  higher  throughout  the  whole  variable  period  than 
when  an  ordinary  solid  positive  carbon  was  used  as  in  curve 
A  A  A,  Fig.  33. 

In  order  to  find  what  influence,  if  any,  a  flat  negative 
carbon  would  have  in  retarding  the  period  at  which  the  P.D. 
became  constant,  cored  and  uncored  normal  positive  carbons 
were  used,  with  flat  uncored  negatives.  In  Fig.  34,  A  A  is 
the  curve  obtained  with  the  uncored,  B  B  that  obtained  with 
the  cored  positive  carbon. 

From  these  curves  it  is  evident  that  the  shape  of  the 
negative  carbon  plays  a  very  small  part  in  the  change  of 
P.D.  that  takes  place  on  starting  the  arc,  for  in  each  case 
the  P.D.  reached  its  steady  value  in  about  8  minutes, 
and  in  neither  case  did  it  deviate  more  than  about  5  volts 
from  that  steady  value,  whereas,  as  has  been  shown,  with 
a  flat  positive  carbon,  the  P.D.  took  about  50  minutes  to 
reach  its  steady  value,  and  it  deviated  by  from  7  to  33  volts 
from  that  steady  value  before  reaching  it. 


P.D.  AFTER  "STRIKING"  THE  ARC. 


109- 


Fig.  35  gives  a  sort  of  bird's-eye  view  of  the  differences 
caused  in  the  change  of  P.D.  after  starting  the  arc  by  using 

(1)  A  A  A,  both  carbons  solid  and  flat. 

(2)  B  BB,  positive  carbon  cored  and  both  flat. 

(3)  B'B',  positive  carbon  cored,  both   normal,  arc  started 
with  cold  carbons. 

(4)  B",  positive  carbon  cored,  both  normal,  arc  started  with 
hot  carbons. 

After  three  minutes  from  starting  the  arc  the  curve  A  A  A 
(Fig.  35)  differs  very  little  from  the  curve  A  A  A  (Fig.  32),  in 
which  the  negative  carbon  was  normal  instead  of  flat,  and 
all  the  other  conditions  were  the  same.  The  reason  there  is  so 
little  appearance  of  'hump '  is,  I  find  on  referring  to  the  labora- 
tory note  books,  that  certain  somewhat  high  P.Ds.  obtained 


P.D.  betu'cen  Carbons  in  Volt* 

s  s  s  s 

,-, 

•^W 

A 

^ 

.   B  , 

B 

10                20                30                40 
Time  in  Minutes. 

FIG.  34. — Current  suddenly  started  and  kept  at  10  amperes.  Length  of 
arc  kept  at  3mm.  A  A,  Carbons :  Positive,  18mm.  solid ;  negative,  15mm. 
solid.  B  B,  Carbons  :  Positive,  18mm.  cored ;  negative,  15mm.  solid. 
Positive  normal,  negative  filed  flat,  in  both  instances. 

between  10  and  35  minutes  after  the  arc  had  been  started  have 
been  omitted  in  drawing  this  curve,  presumably  because  it  was 
supposed  that  these  observations  were  wrong.  Had  points 
corresponding  with  these  somewhat  higher  P.Ds.  been  plotted, 
and  the  curve  A  A  A  (Fig.  35)  drawn  through  the  average  position 
of  all  the  points,  it  would  have  shown  a  hump  such  as  exists 
in  all  the  other  curves  obtained  from  experiments  with  a  flat 
positive  carbon. 

B  B  B  (Fig.  35)  also  differs  very  slightly  from  B  B  B  (Fig.  32) 
in  which  the  negative  was  normal  instead  of  flat ;  in  Fig.  35 
the  curve  starts  with  rather  a  higher  P.D.,  27  instead  of 


110 


THE  ELECTEIC  ARC. 


P.D.  AFTER  "STRIKING"  THE  ARC.  Ill 

25  volts,  and  rises  a  little  more  slowly.  Thus  in  both  this 
and  the  preceding  case  it  is  evident  that  the  difference  made  by 
the  shape  of  the  negative  carbon  is  very  small. 

B'  B'  B'  and  B"  (Fig.  35)  show  how  small  is  the  change  that 
takes  place  in  the  P.Ds.  when  the  arc  is  started  with  both  carbons 
normal,  whether  they  be  hot  or  cold  beforehand.  Started 
cold  the  P.D.  is  about  1J  volts  higher  than  started  hot, 
which  is  what  one  might  have  expected.  The  whole  change 
of  P.D.,  however,  is  very  small,  under  both  circumstances, 
not  more  than  about  1 J  volts  altogether. 

Thus  we  may  gather  from  Figs.  31  to  35  that  the  changes 
that  take  place  in  the  P.D.  of  an  arc  just  after  it  is  started 
are  due  in  order  of  importance  : — 

(1)  To  the  core  of  the  positive  carbon,  if  it  has  one — very 
low  P.D.  at  starting. 

(2)  To  the  shape  of  the  tip  of  the  positive  carbon — the  '  hump.' 

(3)  To  the  shape  of  the  tip  of  the  negative  carbon. 

(4)  Very  slightly  to  the  temperature  of  the  carbons  before 
starting  the  arc. 

Coming  now  to  Question  (4),  to  see  how  changing  the 
length  of  the  arc  affected  the  time  during  which  the  P.D. 
remained  variable  after  the  arc  was  started,  an  18mm.  cored 
positive  carbon  and  a  15mm.  solid  negative  were  again  used, 
the  ends  of  both  carbons  were  filed  flat,  and  the  current  was 
again  kept  constant  at  10  amperes;  but  the  length  of  the 
arc  was  kept  constant  at  6mm.  instead  of  at  3mm.  as  before. 

It  was  found  that  in  this  case,  as  with  the  3mm.  arc,  there 
was  a  very  low  P.D.  at  starting,  a  rise  to  a  maximum,  and 
then  a  slight  fall,  and  finally  the  steady  P.D.  But  the 
whole  series  of  changes,  which  extended,  as  we  have  seen, 
over  a  period  of  55  minutes  with  the  3mm.  arc,  took  only 
20  minutes  with  the  6mm.  arc. 

Next,  to  see  how  varying  the  current  affected  the  time 
during  which  the  P.D.  remained  variable  after  the  arc  was 
started,  an  18mm.  cored  positive  carbon  was  again  used  with  a 
15mm.  solid  negative,  the  ends  of  both  carbons  were  filed  flat, 
the  arc  was  kept  at  the  constant  length  of  3mm. ;  but  a  constant 
current  of  20  amperes  was  maintained,  instead  of  one  of  10 
amperes,  as  in  all  the  previous  experiments  on  the  variation  of 
the  P.D.  with  the  time  after  starting  the  arc. 


112  THE  ELECTRIC  AEC. 

Again  the  curve  obtained  was  found  to  be  of  the  same 
character  as  curve  BBB  (Fig.  35),  with  which,  also,  both 
carbons  were  flat,  and  the  positive  cored ;  only,  with  the  cur- 
rent of  20  amperes  the  changes  were  more  rapid  than  with  that 
of  10  amperes,  and  the  P.D.  became  constant  38  minutes  after 
starting  the  arc,  instead  of  55  minutes  after. 

We  may  gather  from  these  last  two  experiments  that  the 
time    during   which   the   P.D.  between  the  carbons   remains 
variable  after  starting  the  arc  with  flat  carbons  is  longer 
(a)  The  shorter  the  arc, 
(6)  The  smaller  the  current; 
and  thus  Question  (4)  is  answered. 

The  next  question  to  determine  was  what  change  took  place 
in  the  P.D.  between  the  ends  of  the  carbons  when  the  current 
was  suddenly  changed  from  a  lower  to  a  higher  and  from  a 
higher  to  a  lower  value,  the  length  of  arc  being  kept  constant 
during  each  series  of  experiments.  The  experiments,  the  results 
of  which  are  noted  in  the  curves  in  Figs.  36  and  37,  were  made 
in  order  to  answer  this  question. 

These  curves,  as  well  as  all  the  others  published  in  this 
chapter,  are  merely  specimens  of  a  number  of  sets  of  curves 
that  have  been  obtained  under  similar  conditions. 

Since,  at  the  very  first  instant  that  a  change  of  current  is- 
made  the  arc  cannot  have  had  time  to  change  its  cross  section, 
it  would  seem  as  if  at  that  first  moment  the  arc  should  act 
like  a  wire,  and  a  rise  of  potential  should  accompany  an  increase 
of  current,  and  a  fall  of  potential  a  decrease.  In  1893  I  made 
som?  experiments  to  see  if  I  could  detect  this  first  momentary 
similarity  of  sign  between  the  change  of  P.D.  and  change  of 
current,  and  found  that  in  some  cases  it  could  be  easily 
detected,  and  in  others  not  at  all.  Being  pressed  for  time,  T 
did  not  then  continue  the  investigation;  but  when  the  dis- 
cussion about  a  negative  resistance  in  the  arc  arose  in  1896 
(see  p.  75),  I  repeated  the  experiments  with  Mr.  Frith,  for  they 
seemed  to  have  some  bearing  on  the  question.  We  then  found 
that  in  all  cases  where  the  first  momentary  similarity  of  sign 
could  be  perceived,  either  one  or  both  carbons  were  cored.  The 
whole  question  of  the  instantaneous  change  of  P.D.  with  change 
of  current  will  be  discussed  later  on,  in  the  chapter  on  the 
resistance  of  the  arc,  &c. 


SUDDEN  CHANGE  OF  CURRENT. 


113 


A 


(o  < 
10 


d 

1L 


CM 


a 
< 


en 

if 


•^^r^ 


114 


THE  ELECTRIC  ARC. 


The  changes  of  P.D.  in  Figs.  36  and  37  are  very  striking. 
With  wires  one  is  accustomed  to  associate  an  increase  of  current 


8n°A 


with  a  rise  of  potential  and  a  diminution  of  current  with  a  fall. 
But  with  the  arc,  except,  perhaps,  in  the  very  first  instant, 


SUDDEN  CHANGE  OF  CURRENT.       115 

•exactly  the  reverse  takes  place,  and  no  experiments  that  I  know 
of  are  better  calculated  to  impress  upon  one  the  immense 
difference  between  the  way  in  which  a  current  flows  through 
the  arc  and  the  way  in  which  it  flows  through  a  wire  than 
those  from  which  these  curves  were  taken. 

With  the  arc  (with  the  above  exception),  a  sudden  rise  of 
current  is  in  every  case  accompanied  by  a  sudden  fall  of 
potential,  and  a  sudden  fall  of  current  by  a  sudden  rise  of 
potential,  even  when,  as  in  the  case  of  an  arc  of  1mm.  with 
a  cored  positive  carbon  (lower  curves,  Fig.  36),  the  final  steady 
value  of  the  P.D.  is  higher  with  the  larger  current  than  with 
the  smaller. 

Indeed,  in  nearly  every  case  the  P.D.  overshoots  the  mark, 
as  it  were,  and  goes  much  lower  with  an  increase  of  current, 
and  much  higher  with  a  diminution,  than  its  own  final  steady 
value.  This  exaggeration  of  the  decrease  and  increase  of  P.D., 
which  is  very  marked  when  the  currents  are  small,  becomes  less 
and  less  marked  as  the  currents  increase  in  value,  until  finally, 
with  currents  of  30  amperes  and  over,  it  ceases  to  exist  with 
the  carbons  we  have  tried,  and  the  P.D.  remains  practically 
constant,  whether  the  current  is  changed  suddenly  or  gradually. 
In  fact,  when  we  get  on  to  the  flat  part  of  the  curves  con- 
necting P.D.  with  current  for  constant  lengths  of  arc  (Chap.  IV., 
pp.  121  to  130)  the  P.D.  is  practically  a  constant,  however 
quickly  or  slowly  the  current  may  be  changed. 

The  curves  in  Fig.  36,  the  upper  of  which  is  for  a  solid 
and  the  lower  for  a  cored  positive  carbon,  show  that  the 
excessive  sudden  rise  and  fall  of  P.D.  with  a  sudden  diminution 
and  increase  of  current  does  not  depend  entirely  upon  the  core, 
for  it  takes  place  in  both  sets  of  curves  alike,  although  it  is 
.more  marked  in  the  lower. 

The  upper  curves  are  a  little  deceptive,  because  the  hissing, 
which  took  place  in  this  particular  experiment  at  15  amperes, 
lowered  the  P.D.  considerably,  quite  apart  from  the  sudden 
change  of  current. 

Some  experiments  I  have  made  since  these,  as  well  as  the 
above  curves,  amply  verify  the  following  deductions.  With  a 
sudden  change  of  current : — 

(1)  The  sudden  change  of  P.D.  is  greater  with  a  cored  than 
with  a  solid  positive  carbon; 

i2 


116  TEE  ELECTRIC  ARC. 

(2)  The  subsequent  slow  rise,  or  fall,  of  P.D.  is  greater  with 
a  cored  than  with  a  solid  positive  carbon; 

(3)  The  time  during  which  this  slow  change  of  P.D.  takes 
place  is  greater  with  a  cored  than  with  a  solid  positive  carbon. 

The  curves  in  Fig.  37  show,  although  not  to  a  very  marked 
extent,  that  the  time  the  P.D.  takes  to  reach  its  steady  value 
after  a  sudden  change  of  current  is  less  with  a  longer  than 
with  a  shorter  arc.  Experiments  made  later  prove  this  point  quite 
conclusively.  For  instance,  with  an  18mm.  cored  positive 
carbon  and  a  15mm.  solid  negative,  arcs  of  6mm.  and  1mm., 
respectively,  were  maintained.  The  current  was,  in  each  case, 
kept  first  at  4  amperes,  and,  when  the  P.D.  had  become  steady 
for  that  current,  it  was  suddenly  changed  to  9  amperes,  and 
kept  constant  at  that  value  till  the  P.D.  had  become  steady. 
It  was  found  that,  after  suddenly  altering  the  current  from  4 
to  9  amperes,  the  time  that  elapsed  before  the  P.D.  assumed 
its  steady  value  for  9  amperes  was  9  minutes  in  the  ease  of  the 
6mm.  arc,  and  16  minutes  in  that  of  the  1  mm.  arc. 

These  sudden  exaggerated  changes  of  P.D.  probably  depend 
upon  the  difference  between  the  shapes  of  the  carbons  and 
craters  with  small  and  large  currents,  an  idea  which  i» 
strengthened  by  the  fact  that  with  very  large  currents  the 
shapes  of  the  carbons  alter  very  slightly  with  a  change  of 
current,  and,  as  we  have  just  seen,  the  P.D.  also  scarcely 
alters. 

It  is  probable  that  the  action  is  as  follows  :  It  has  been 
shown  (Chap.  I.,  p.  13)  that  with  a  large  current  both 
carbons  are  burnt  away  much  farther  down  than  with  a 
small  current,  thus  making  the  lengths  of  the  pointed  parts 
of  the  carbons  shorter  the  smaller  the  current.  Hence,  when  a 
small  current  has  been  flowing  through  the  arc  for  some  little 
time,  the  carbons  are  very  blunt,  and  the  larger  amount  of 
volatile  carbon  sent  off  by  the  larger  current  when  it  is  suddenly 
switched  on  will  be  squeezed  out  laterally,  thus  making  the 
cross  section  of  the  arc  abnormally  great,  and  its  resistance 
exceptionally  small;  therefore,  the  P.D.  necessary  to  keep  the 
current  flowing  will  be  below  the  steady  value.  Then  as 
the  points  of  the  carbons  burn  away  and  become  tapered 
under  the  influence  of  the  larger  current,  the  volatile  carbon 
can  stretch  out  more  lengthwise,  and  gradually  take  its  normal 


SUMMARY.  117 

form  for  the  larger  current,  and  at  the  same  time  the  P.D.  rises 
to  its  final  steady  value. 

Similarly,  when  a  small  current  was  turned  on  after  a  large 
current  had  been  flowing  for  some  time,  the  volatile  carbon 
would  at  first  be  too  much  elongated  owing  to  the  ends  of  the 
carbons  being  much  tapered,  and  as  these  burnt  away  and  became 
blunter  the  volatile  carbon  would  be  squeezed  out  more 
laterally,  the  cross  section  of  the  arc  would  be  increased,  and 
the  P.D.  would  fall  to  its  final  steady  value. 

The  exaggerated  change  of  P.D.  when  the  current  is  sud- 
denly altered  depends  in  another  way  also  on  the  tips  of  tbe 
•carbons  being  blunter  with  small  currents  than  with  large 
ones.  For  the  mean  distance  of  the  tips  of  the  carbons  from 
one  another  is  less  when  they  are  blunt,  i.e.,  normal  for  a  small 
current,  than  when  they  are  pointed,  i.e.,  normal  for  a  large  one, 
even  although  the  length  of  the  arc  is  maintained  the  same  in 
both  cases  (see  definition  of  length  of  arc,  p.  99).  Hence  the 
mean  length  of  the  arc  must  also  be  less  in  the  first  case  than 
in  the  second.  But  if  the  mean  length  of  the  arc  is  less,  the 
P.D.  r  ecessary  to  maintain  a  given  current  flowing  through  the 
arc  will  be  less,  all  other  conditions  being  the  same.  Therefore 
the  P.D.  necessary  to  maintain  a  large  current  flowing  through 
an  arc  of  given  length  will  be  less  when  the  carbons  are  normal 
for  a  small  current  than  when  they  are  normal  for  a  Large  one, 
and  vice  versd. 


SUMMARY. 

I.  After  the  arc  has  been  maintained  of  a  constant  length 
and  with  a  constant  current  flowing  for  a  certain  time,  the 
P.D.  between  the  carbons  finally  becomes  constant  also. 

II.  The  time  that  elapses  before  the  P.D.  becomes  constant 
is  less : 

(1)  The  more  nearly  the  original  shapes  of  the  carbons 
approximate  to  the  shapes  they  finally  take  when  the  P.D. 
becomes  constant ; 

(2)  The  longer  the  given  arc ; 

(3)  The  greater  the  value  of  the  constant  current 


118  THE  ELECTRIC  ARC. 

III.  The   time   that   elapses   before  the  P.D.   assumes   ite 
constant  value  is  less  and  the  P.D.  is  greater  with  solid  than 
with  cored  carbons. 

IV.  When  the  current  is  suddenly  changed  from  a  higher 
to  a  lower,  or  a  lower  to  a  higher  value,  the  P.D.  between  the 
carbons  increases   or   diminishes   to  a  value   greater   or   less 
respectively  than  its  final  constant  value  for  the  new  current, 
and  then  gradually  falls  or  rises  to  that  constant  value. 

V.  This  first  excessive  increase  or  diminution  is  greater  the 
greater  the  difference  between  the  original  and  final  current. 

VI.  For  a  given  sudden  change  of  current  the  first  excessive 
increase  or  decrease  of  P.D.  is  greater  the  smaller  the  original 
current,  while  with  large  currents  it  is  practically  non-existent. 

VII.  When  a  cored  positive  carbon  is  used  the  P.D.  is  some- 
times as  low  as   16  volts  for  a  short  time,  with  a  perfectly 
silent  arc. 

VIII.  With  a  cored  positive  carbon  the  change  of  P.D.  is 
sometimes  observed  to  be  in  the  same  direction  as  the  corres- 
ponding sudden  change  of  current,  for  the  first  instant.     This 
first  increase  of  P.D.  with  an  increase  of  current  and  decrease  of 
P.D.  with  a  diminution  of  current  has  never  been  observed 
with  solid  carbons. 


CHAPTER  IV. 


CURVES  CONNECTING  THE  P.D.  BETWEEN  THE  CARBONS  WITH  THE 
CURRENT  FLOWING  FOR  CONSTANT  LENGTHS  OF  ARC,  AND 

CURVES  CONNECTING  THE  P.D.  BETWEEN  THE  CARBONS  WITH 
THE  LENGTH   OF   THE   ARC    FOR  CONSTANT   CURRENTS. 

When  Prof.  Ayrton  first  directed  his  attention  to  obtaining 
a  series  of  observations  of  the  arc  which  would  enable  him  to 
form  curves  connecting  any  two  of  the  variables,  while  a  third 
was  kept  constant,  the  three  variables  of  which  direct  observa- 
tions were  made  were  the  P.D.  between  the  carbons,  the 
current  flowing,  and  the  length  of  »the  arc.  From  these  the 
apparent  resistance  and  the  power  consumed  in  the  arc  could 
also  be  found.  Most  of  the  experiments  were  made  with 
cored  positive  and  solid  negative  carbons ;  but  a  single  set  of 
results  was  obtained  with  both  carbons  cored,  and  another  with 
both  carbons  solid,  in  order  to  see  what  variations  in  the 
curves  these  changes  produced. 

When  beginning  to  study  the  arc  on  my  own  account,  it 
appeared  to  me  that  it  would  be  better  to  avoid  the  com- 
plications arising  from  the  use  of  cored  carbons,  and  to  study 
the  problems  under  their  simplest  conditions  by  employing 
none  but  solid  carbons.  Accordingly,  my  experiments  were 
conducted  with  solid  carbons  for  both  positive  and  negative, 
the  positive  carbon  being  llmm.  and  the  negative  9mm.  in 
diameter  in  all  cases. 

The  make  of  carbon  employed  was  the  "  Apostle,"  the  same 
as  had  been  used  in  all  the  investigations  carried  out  under 
Prof.  Ayrton's  direction,  so  that  the  results  obtained  with 
solid  carbons  might  be  compared  with  those  obtained  when  a 
cored  positive  carbon  was  used. 

As  the  relations  existing  between  the  variables  of  the  arc 


120 


THE  ELECTRIC  ARC. 


'stl<>A  w? 


CONSTANT  LENGTHS  OF  AEC. 


121 


are  undoubtedly  simpler  when  both  carbons  are  solid,  it  -will 
be  best  to  examine  the  curves  for  solid  carbons  (Fig.  38)  first. 
The  values  used  in  plotting  the  curves  in  Fig.  38  were  the 
means  of  the  results  obtained  on  different  days  with  different 
pairs  of  llmm.  and  9mm.  solid  carbons,  and,  in  order  to 
indicate  to  what  extent  these  means  differed  from  the  actual 
observations,  a  sample  is  appended,  in  Table  XL,  of  the 
actual  results  that  were  obtained  when  the  arc  was  5mm.  in 
length  : — 

Table  XL — Specimen  of  the  Actual  Daily  Results  obtained  when 

the  Arc  ivas  5mm.  long. 
Carbons  both  solid.     Positive,  llmm. ;  negative,  9mm. 


Current 
in 
amps. 

Potential  Difference  between  Carbons  in  Volts. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

Mean  of  the 
7  days'  results. 

1-96 
2-45 
2-95 
3-45 
3-96 
4-46 
4-97 
5-47 
5-97 
6-47 
6-97 
7-97 
9-0 
10-07 
11-07 
12-07 
14-06 
16-04 
18-03 
'^0-0 
22-0 
26-0 

84-4 
77-1 
73-1 
67-7 
66-3 
64-8 
62-8 
61-3 
58-9 

57-9 
57-4 
56-0 

84-9 

84-65 
75-1 
71-65 
67-7 
65-9 
64-45 
62-64 
61-4 
59-77 
59'4 
58-5 
57-4 
56-4 
56-0 
55-0 
54-8 
54-0 
52-5 
53-5 
53-0 
43'0 
43-0 

... 

... 

73-1 
70-2 

... 

... 

65-5 
64-5 
63-0 

62:8 
61-7 
60-7 
59-9 
69-2 
53-0 
57-0 
56-4 

... 

64-8 
63-0 
62-0 

63-7 
61-6 
60-7 
59-7 
58-9 
584 
57-0 
56-0 

57:2 
56-5 
55-5 
55-0 
54-3 
53-5 
52-5 

... 

55-2 
54-4 

... 

... 

... 

... 

53-5 
53-0 
A3-0 

... 

... 

43-0 

The  numbers  in  italics  refer  to  hissing  arcs. 

The  numbers  in  any  one  column  in  Table  XL  are  the 
results  of  the  experiments  carried  out  in  a  single  day  with  a 
5mm.  arc,  and,  although  the  carbons  did  not  require  to  be 
changed  each  day,  sometimes  a  new  positive  and  sometimes  a 
new  negative  carbon  had  to  be  inserted,  so  that,  on  the  whole, 


122 


THE  ELECTRIC  AEC. 


about  three  different  positive  and  three  different  negative 
carbons  were  used  in  obtaining  the  numbers  given  in  the  last 
column  of  this  Table. 

Table  XII.  gives  the  means  of   the  whole  series  of  results 
from  which  the  curves  in  Fig.  38  were  plotted. 

Table  XII. — Means  of  the  Experimental  Results  used  in  Plotting 
the  Curves  in  Fig.  38.  Carbons  both  solid.  Positive^ 
llmm. ;  negative,  9mm. 


Cur- 
rent in 
amps. 

1=1. 

P.D.  in 

volts. 

1=2. 
P.D,  in 

volts. 

Z=3. 
P.D.  in 

volts. 

Z  =  4. 
P.D.  in 

volts. 

1  =  5. 
P.D.  in 

volts. 

1=6. 
P.D.  in 

volts. 

1  =  7. 
P.D.  in 
volts. 

1-96 

50-25 

60-0 

67-0 

79-5 

84-6 

2-46 

48-7 

55-75 

62-75 

67-7 

75-1 

82-0 

85V9 

2.97 

47-9 

53-5 

59-75 

65-0 

71-7 

76-1 

,81-0 

3-45 

47-5 

52-0 

58-5 

63-0 

67-7 

72-4 

77-0 

3'96 

46-8 

51-2 

56-0 

61-0 

65-9 

69-6 

75-1 

4-46 

45-5 

50-6 

54-5 

59-0 

64-45 

67-5 

71-25 

4-97 

45-7 

49-8 

53-5 

58-25 

62-6 

65-9 

70-25 

5-47 

... 

52-75 

57-25 

61-4 

64-6 

68-2 

5-97 

45-0 

49-0 

52-0 

56-25 

59-75 

63-1 

67-3 

6'47 

... 

.  . 

c  .  . 

59-4 

62-4 

66-55 

6-97 

44-0 

48-1 

51-4 

55-1 

58-5 

61-4 

65-65 

7-47 

61-1 

64-65 

7-97 

43-6 

47-4 

50-6 

54-3 

57'4 

60-5 

64-2 

8-48 

..  . 

63-25 

9-0 

43-5 

50-2 

53-5 

56-3 

59-5 

626 

10-07 

42-8 

46-b 

49-8 

53-0 

56-0 

58-8 

61-5 

11-07 

... 

55-0 

58-2 

12-07 

42-35 

45-5 

48-5 

51-75 

54-8 

57-6 

60-35 

14-06 

42-2 

45-0 

... 

50-6 

54-0 

56-8 

59-5 

16-05 

... 

... 

52-5 

56-0 

58-75 

16-55 

44-5 

... 

... 

... 

16-85 

si-o 

... 

... 

... 

17-54 

... 

S8'4 

47-5 

... 

17-64 

... 

... 

... 

49-4 

... 

... 

18-03 

... 

SS'O 

... 

53-5 

... 

... 

18-53 

... 

38:5 

... 

... 

19-0 

... 

... 

SS'O 

... 

... 

... 

19-22 

... 

... 

... 

50-0 

... 

t 

... 

19-42 

... 

55-5 

... 

200 

S4'5 

SS'O 

... 

53-0 

20-5 

... 

... 

... 

39-3 

... 

55-5 

... 

21-0 

,. 

... 

56-9 

22-0 

... 

..  . 

43-0 

46-5 

... 

23-0 

48-0 

25-0 

... 

34:5 

36-5 

40-0 

..  . 

26-0 

... 

43-0 

47-0 

29-97 

... 

... 

40-5 

46'0 

48'0 

The  numbers  in  italics  refer  to  hissing  arcs. 


CONSTANT  LENGTHS  OF  ARC.  123 

These  curves  connect  the  P.D.  between  the  carbons  with  the 
current  flowing  for  the  various  constant  lengths  of  arc,  with  solid 
carbons.  Each  point  on  each  curve  represents  the  P.D. 
between  the  carbons  after  the  current  had  been  kept  flowing 
at  its  specified  value  for  a  considerable  time,  and  the  length  of 
the  arc  kept  at  its  specified  value  during  the  whole  of  that 
time.  The  carbons  had  thus  acquired  their  normal  shape 
for  the  particular  current  and  length  of  arc.  The  time  required 
for  this  varies  from  about  10  minutes  to  over  two  hours  under 
different  circumstances.  It  was  the  want  of  appreciation  of 
the  very  long  time  that  it  is  necessary  in  certain  cases  to  keep 
the  current  and  length  of  arc  constant  before  the  carbons 
acquire  their  final  shape,  that  led  to  so  much  labour  being 
wasted  in  1890,  in  obtaining  the  looped  curves  for  ascending 
and  descending  currents,  of  which  Fig.  30,  Chap.  III.,  is  a 
specimen. 

The  general  character  of  the  curves  indicates  an  inverse 
connection  between  the  P.D.  and  current  for  any  given  length 
of  arc.  That  is  to  say,  the  P.D.  diminishes  as  the  current 
increases.  It  diminishes  rapidly  with  small  currents,  and 
more  and  more  slowly  as  the  current  increases,  never,  however, 
becoming  constant  with  solid  carbons.  Take,  for  example,  the 
5mm.  arc.  With  an  increase  of  current  of  4  amperes — from  2 
to  6  amperes — the  P.D.  falls  23  volts — from  83  to  60  volts ; 
with  a  further  increase  of  5  amperes — from  6  to  1 1  amperes — 
'  the  P.D.  falls  only  5  volts,  and  with  a  still  further  increase  of 
9  amperes — from  11  to  20  amperes — it  falls  only  2'5  volts. 
Thus  the  P.D.  never  becomes  constant,  but  it  falls  very  slowly 
as  the  hissing  point — the  point  at  which  the  current  is  so  large 
that  any  increase  would  cause  the  arc  to  hiss — is  approached. 
The  position  of  these  hissing  points,  which  evidently  varies 
with  the  length  of  the  arc,  will  be  discussed  in  the  chapter 
on  hissing. 

The  curves  for  the  shorter  arcs  are  much  less  steep  than 
those  for  the  longer  ones ;  but  from  their  shape  it  is  evident 
that  this  is  only  because  the  steeper  parts  of  the  curves  for 
short  arcs  would  belong  to  smaller  currents  than  2  amperes, 
the  smallest  used.  In  other  words,  the  ratio  cf  change  of  P.D. 
to  change  of  current  is  greatest,  not  only  when  the  current  is 
least,  but  also  when  the  arc  is  longest. 


124  THE  ELECTE1C  AEG. 

For  instance,  in  the  5mm.  arc  (Fig.  38),  when  the  current 
starts  at  2  amperes,  an  increase  of  4  amperes  is  accompanied 
by  a  fall  of  23  volts  in  the  P.D.  between  the  carbons,  but 
in  the  1mm.  arc,  when  the  current  starts  at  2  amperes,  a  rise 
of  4  amperes  is  accompanied  by  a  fall  of  only  6  volts.  It 
would  be  necessary,  indeed,  for  the  current  to  start  at  1  ampere, 
or  even  less,  with  an  arc  of  1mm.,  for  a  rise  of  4  amperes  to  be 
accompanied  with  so  great  a  fall  of  the  steady  P.D.  as  23  volts. 

In  their  Paper  read  before  the  Physical  Society  in  1882 
{Proc.  Phys.  Soc.,  Vol.  V.,  p.  197)  on  "The  Resistance  of  the 
Electric  Arc,"  Messrs.  Ayrton  and  Perry  said,  in  speaking  of  the 
curve  given  in  that  Paper,  which  they  had  drawn  from  the 
results  of  their  experiments  connecting  the  P.D.  between 
the  carbons  with  the  length  of  the  arc  with  solid  carbons 
for  arcs  up  to  31mm.  long:  "The  curve  we  have  obtained 
is  also  strikingly  like  that  obtained  by  Drs.  W.  De  La  Rue 
and  Hugo  Mliller  for  the  connection  between  the  electro- 
motive force  and  the  distance  across  which  it  would  send 
a  spark.  Those  gentlemen  also  made  experiments  on  the  elec- 
tric arc  with  their  large  battery.  4  .  .  The  result  of  an 
experiment  in  air  between  two  brass  points  is  given ;  but, 
according  to  that,  when  the  arc  was  half  an  inch  in  length  the 
difference  of  potential  between  the  brass  points  was  about  700 
volts.  How  far  the  very  high  electromotive  force  found  by 
Drs.  W.  De  La  Rue  and  Hugo  Miiller  to  be  necessary  in  this 
case  arose  from  a  combination  of  the  material  employed  for  the 
electrodes  and  the  smallness  of  the  diameter  of  the  brass  elec- 
trodes, or  whether  the  law  that  '  the  electromotive  force  neces- 
sary to  maintain  an  arc  depends  mainly  on  the  length  of  the  arc, 
and  hardly  at  all  on  the  strength  of  the  current,'  fails  when  the 
current  is  below  a  certain  small  limit,  we  are  unable  to  say; 
but  of  course  both  the  diameter  of  the  brass  electrodes  they 
employed  and  the  strength  of  the  current  that  was  passing 
(0'025  ampere)  in  the  arc  was  very  much  less  than  that  used 
in  any  ordinary  electric  light,  to  which  the  experiments  of 
Mr.  Schwendler  and  ourselves  especially  refer.  It  is  very  pro- 
bable that  the  difference  in  the  material  of  the  electrodes  has 
mainly  to  do  with  the  difference  between  their  results  and 
ours ;  and  we  think  it  very  probable  that,  with  very  sofb 
carbons,  an  arc  of  a  given  length  could  be  maintained  with  a 


P.D.  CURRENT  AND  LENGTH  OF  ARC. 


125 


much  less  difference  of  potentials  than  that  found  by  us,  since 
it  would  be  more  easy  for  a  shower  of  carbon  particles  to  be 
maintained  between  the  ends  of  the  carbons." 

Two  results  are  here  foreshadowed,  which  have  both  since 
been  verified,  the  one  that  the  P.D.  for  a  given  current  and 
length  of  arc  would  be  found  to  be  smaller  if  the  carbons  were 
made  softer,  the  other  that  the  P.D.  for  a  given  length  of  arc 
would  be  far  higher  with  very  small  currents  than  with  those 
which  are  used  practically  with  an  arc  lamp.  The  first  result 

Table  XIII. — Means  of  the  Experimental  Results  used  in  Plotting 
the  Curves  in  Fig.  39.  Positive  carbon,  18mm.,  cored; 
negative  carbon,  15mm.,  solid. 


Cur- 
rent in 
amps. 

1=0-5 
P.D.  in 

volts. 

1  =  1 
P.D.  in 

volts. 

1  =  2 
P.D.  in 

volts. 

l=7> 
P.D.  in 

volts. 

1  =  4 
P.D.  in 

volts. 

1  =  5 
P.D.  in 

volts. 

1  =  6 
P.D.  in 

volts. 

4-0 

... 

37-0 

... 

... 

5-0 

49-3 

... 

... 

6-0 

33-0 

36-0 

47-0 

50-5 

53-0 

54-75 

59-5 

7'8 

34-5 

... 

... 

8-0 

345 

36-0 

55-0 

10-0 

... 

43-0 

46-5 

47-5 

49-75 

11-0 

361 

... 

... 

12-0 

35V0 

... 

... 

... 

15-0 

... 

... 

42-0 

44-5 

46V5\ 
46'OJ 

48-0 

49-5- 

16-0 

... 

... 

44-0 

... 

... 

17-0 

381 

... 

... 

... 

18-0 

38V0 

... 

... 

20-0 

38-75 

42-0 

44V0 

... 

48-0 

22-0 

... 

... 

43V5 

... 

23-0 

39-75 

... 

..  . 

... 

... 

24-0 

39-0 

... 

... 

... 

... 

25-0 

... 

... 

... 

44V2 

46-0 

48V0" 

27-5 

... 

40-0 

... 

28-0 

... 

... 

43-0 

... 

30-0 

... 

40V0 

41-5 

43-0 

44-2 

45-5 

48-a 

33-0 

40-1 

... 

... 

... 

34-0 

39-5 

... 

... 

... 

35-0 

... 

IM 

... 

44-0 

45-4 

47-7 

40-0 

40V0 

40-9 

... 

43-9 

45-75 

47-5 

41-0 

... 

... 

43-0 

45-0 

... 

... 

... 

46-0 

47-5 

47-0 

... 

... 

43-0 

43-9 

47-25 

... 

43-2 

... 

47-5 

33-0 

... 

... 

... 

48-0 

... 

35-0 

... 

... 

48-75 

... 

42-5 

... 

... 

The  numbers  in  italics  refer  to  hissing  arcs. 


126 


THE  ELECTRIC  ARC. 


was  found  to  be  true  when  cored  carbons  were  subsequently 
manufactured,  and  the  second  is  borne  out  by  the  strikingly 
rapid  rise  in  the  curves  in  Figs.  38,  39,  40  and  41,  as  the  current 
becomes  very  small. 

In  fact,  for  very  small  currents,  whether  one,  or  both,  or 
neither  of  the  carbons  be  cored,  the  P.D.  falls  rapidly  with 
increase  of  current,  probably  on  account  of  a  small  current  arc 
presenting  a  large  cooling  surface  in  proportion  to  its  cross- 
section. 

Tables  XIIL,  XIV.  and  XV.  give  the  results  of  the  experiments 
made  by  students  of  Professor  Ayrton  at  the  Central  Technical 
College,  London,  with  cored  positive  and  solid  negative  carbons. 
Each  number  gives  the  mean  of  several  observations. 

Table  XIV. — Experimental  Results  used  in  Plotting  the  Curves  in 
Fig.  JfO-  Positive  carbon,  13mm.,  cored ;  negative  carbon, 
llmm.,  solid. 


Cur- 
rent in 
amps. 

1  =  0. 
P.D.  in 

volts. 

1=1. 
P.D.  in 

volts. 

1  =  2. 
P.D.  in 

volts. 

1  =  3. 
P.D.  in 

volts. 

2=4. 
P.D.  in 

volts. 

1=8. 
P.D.  in 

volts. 

1=8. 

P.D.  in 

volts. 

2-0 

47-1 

... 

71-2 

2-5 

56-0 

63-0 

2-8 

42-0 

fm 

3-0 

40-5 

56-5 

61-5 

62-0 

64-5 

76-2 

4-0 

... 

39-5 

... 

58-25 

69-5 

4-5 

... 

49-0 

... 

5-0 

... 

... 

56-5 

{CC.fl  \ 

... 

6-0 

35-0 

37-5 

46-0 

50-2 

DO  U  \ 

54-0  1 
52-7  f 

55-0 

63-3 

52-4  J 

8-0 

35-5 

... 

... 

... 

9-9 

... 

39-0 

43-0 

f47-5j 
\46-5/ 

(  49-2^1 
\  49-7  \ 
[50-2  j 

52-0 

(607 
159-2 

12-0 

37-0 

... 

... 

<t 

13-0 

... 

43-0 

... 

... 

... 

15-0 

.. 

... 

... 

... 

.1  47-4  7 
H7-7J 

... 

... 

16-0 

38-0 

... 

(45-2) 
144-7J 

... 

50'2 

54-7 

19-4 

... 

... 

43-0 

... 

... 

19-9 

40-0 

41-0 

... 

... 

47-5 

49'2 

/64D 

\52-5 

21-0 

... 

... 

44-5 

... 

... 

23-7 

... 

... 

... 

46-5 

25-0 

... 

... 

... 

46-5 

••*• 

53-5 

27-5 

45-2 

27-9 

41-5 

42-5 

43-5 

... 

29-9 

... 

... 

45V2 

46-6 

48-6 

... 

P.D.  CUREENT  AND  LENGTH  OF  ARC. 


127 


Table  XV. — Experimental  Results  used  in  Plotting  the  Curves 
in  Fig.  41-  Positive  carbon,  9mm. ,  cored  ;  negative  carbon, 
8mm.,  solid. 


1  =  0. 

1  =  0-5 

1  =  1. 

1  =  2. 

Cur- 
rent in 
amps. 

P.D.  in 

volts. 

Current 
in 
amps. 

P.D.  in 

volts. 

Current 
in 
amps. 

P.D.  in 

volts. 

Current 
in 
amps. 

P.D.  in 

volts. 

1-8 

33-5 

2-4 

38-5 

3-0 

48-4 

3-0 

52-5 

2-2 

30-0 

3-0 

35-8 

3-5 

46-0 

3-1 

51-5 

2-3 

29-2 

4-0 

35-6 

4-9 

42-0 

4-0 

48-5 

30 

29-0 

5-9 

37-5 

6-9 

42-0 

5-9 

44-3 

5-3 

30-0 

7-8 

37-5 

8-8 

41-5 

8'8 

43-5 

7-8 

32-5 

9-8 

39-5 

121 

42-6 

10-0 

44-1 

11-3 

36-0 

12-1 

39-0 

15-2 

43-0 

121 

43-6 

13-4 

37-5 

13-2 

40-5 

15'5 

43-0 

15-2 

44-2 

15-0 

38-6 

14-5 

40-5 

19-0 

34-0 

15-5 

44-0 

15-5 

38-6 

21-3 

31-7 

22-3 

33'8 

19-2 

36-0 

18-3 

29-8 

30-3 

32'5 

25-3 

34'4 

22-3 

35-5 

25-0 

29'8 

30-3 

34'5 

26-3 

35'5 

30-0 

29'8 

... 

... 

30-3 

36'0 

1-- 

=  3. 

1  = 

4. 

1  = 

5. 

1= 

=  8. 

Cur- 

P.D. in 

Current 

P.D.  in 

Current 

P.D.  in 

Current 

P.D.  in 

rent  in 
amps. 

volts. 

in 
amps. 

volts. 

in 
amps. 

volts. 

in 
amps. 

volts. 

3-5 

55-2 

3-0 

59-0 

3*5 

61-1 

3-5 

69-0 

4-5 

51-7 

4-0 

57-7 

4-0 

60-1 

4-9 

64-5 

59 

48-5 

5-9 

54-0 

5'9 

55-8 

7-8 

60-0 

8-3 

47-0 

8-8 

51-7 

8-8 

52-6 

12-2 

56-0 

12  I 

45-5 

12-0 

49-0 

12-2 

50-5 

16-4 

55-0 

17-2 

46-0 

15-5 

48-7 

16-2 

50-2 

17-0 

55-0 

17-5 

46-0 

17-0 

48-7 

17-2 

50-0 

20-0 

55-0 

21-0 

37'5 

17-2 

48-4 

18-3 

50-5 

22-0 

55-5 

2  VI 

3T5 

19-0 

48-4 

19-2 

50-9 

25-0 

55-5 

?6'3 

37-5 

20-5 

48-3 

19-5 

51-0 

28-3 

49-2 

30-3 

37'5 

24-0 

40-2 

23-3 

41-5 

30-3 

49'2 

... 

25-5 

40-2 

25-3 

41-6 

34-0 

49-2 

... 

30-3 

40-0 

30-3 

41-5 

The  numbers  in  italics  refer  to  hissing  arcs. 

On  comparing  the  curves  in  Figs.  39,  40,  and  41  with  those 
for  solid  carbons  in  Fig.  38,  one  very  curious  point  in  common 
may  be  noticed,  viz.,  if  the  P.D.  between  the  carbons  be  kept 
constant^  and  the  arc  be  lengthened  and  maintained  at  the  greater 


128 


THE  ELECTRIC  AEC. 


CONSTANT  LENGTHS  OF  ARC. 


129 


•SWA 


130 


THE  ELECTRIC  AEG. 


£  S 


CONSTANT  LENGTHS  OF  ARC.  131 

length,  the  current  is  larger  and  not  smaller  than  it  ivas  for  the 
shorter  length  of  arc.  For  example,  a  given  P,D.,  say  50  volts, 
sends  a  current  of  4*1  amperes  through  an  arc  2mm.  long 
(Fig.  40),  6-2  amperes  through  an  arc  3mm.  long,  9-6  amperes 
through  one  of  4mm.,  and  16*4  amperes  through  one  of  5mm., 
all  the  arcs  being  silent.  Or,  dividing  this  P.D.  of  50  volts 
by  these  currents,  it  follows  that  the  apparent  resistances  of  the 
2,  3,  4,  and  5mm.  arcs  for  this  P.D.  are  12-2,  8-1,  5'2  and 
3  ohms  respectively.  Hence,  for  a  constant  P.D.,  the  apparent 
resistance  of  the  silent  arc,  when  in  the  normal  condition, 
diminishes  rapidly  as  the  arc  is  lengthened. 

Although  the  curves  in  Figs.  39,  40,  and  41  bear  a  certain 
resemblance  to  those  for  solid  carbons  in  FJg.  38,  yet  there  are 
important  differences  between  the  two,  the  chief  of  which  con- 
cerns the  change  of  P.D.  with  change  of  current.  With  a 
solid  positive  carbon  (Fig.  38),  as  already  mentioned  (p.  123), 
the  P.D.  falls  continuously  as  the  current  increases,  but  with 
a  cored  positive  carbon  the  P.D.  generally  falls  to  a  minimum 
and  then  rises  again,  as  was  first  shown  by  Nebel.  Even 
when  the  P.D.  does  not  appear  to  rise  after  reaching  a 
minimum,  as  in  the  longer  arcs  with  the  larger  sizes  of 
carbons  (Figs.  39  and  40),  it  is  probable  that  if  the  curves 
had  been  continued  till  the  hissing  point  was  reached, 
an  increase  of  P.D.,  as  the  curve  neared  the  hissing  point, 
would  have  been  observed,  for  it  is  noticeable  that  all  the  curves 
in  Figs.  39  and  41,  which  have  been  completed  up  to  the  hissing 
point,  except  the  4mm.  curve  in  Fig.  41,  which  is  probably 
erroneous,  show  the  P.D.  falling  to  a  minimum  and  then  rising. 

This  minimum  corresponds  with  a  larger  and  larger  current 
the  longer  the  arc,  as  was  also  pointed  out  by  Nebel  in  1886, 
although  he  had  no  idea  that  this  form  of  curve  depended  upon 
the  use  of  a  cored  positive  carbon.  The  minimum  also  seems 
to  correspond  with  a  larger  current  the  greater  the  diameters 
of  the  carbons.  For  instance,  the  minimum  P.D.  for  a  2mm. 
arc  seems  to  be  reached  with  a  current  of  about  15  amperes 
when  carbons  18mm.  and  15mm.  are  used,  but  with  a  current 
of  about  7  amperes  when  carbons  9mm.  and  8mm.  in 
diameter  are  used.  Thus  it  is  possible  that  with  long  arcs 
between  thick  carbons  the  minimum  P.D.  might  correspond 
with  such  a  large  current  that  hissing  would  begin  before  that 

K2 


132 


THE  ELECTRIC  AUG.. 


current  was  reached.  In  this  case  the  P.D.  would  continue  to 
fall  or  remain  practically  constant  till  hissing  began. 

Whether  the  P.D.  ever  attains  its  minimum  and  rises  again 
or  not,  with  long  arcs  and  large  carbons  it  alters  so  slowly  that 
it  may  be  considered  constant  over  a  wide  range  of  current. 

In  1879  the  late  Mr.  Schwendler  published  the  then  new 
statement  that  the  P.D.  between  the  carbons  for  a  fixed 
length  of  arc  was  independent  of  the  current.  This  result  was 
confirmed  by  Profs.  Ayrton  and  Perry,  for  currents  that  were 
fairly  large  for  the  carbons  employed  and  for  the  length  of 
the  arc  (Proc.  Phys.  Soc.,  1882,  Vol.  V.,  p.  197).  That  it  is  not 
quite  true  for  solid  carbons  we  have  already  seen,  but  the 
curves  in  Figs.  39,  40  and  41  show  that  Mr.  Schwendler's  result 
is  true  for  long  arcs  when  the  positive  carbon  is  cored. 


70 


CO 


£  55 

i 

^50 


6  8  10  12 

Current  in  Amperes. 


14 


10 


18 


20 


FIG.  42.— 4mm.  arc — A  A  A :  Positive,  9mm.,  solid  ;  negative,  8mm.,  solid. 
B  B  B,  Positive,  9mm.,  cored  ;  Negative,  8mm.,  solid. 

The  curves  in  Fig.  42  were  drawn  in  order  to  see  at  a  glance 
what  was  the  general  character  of  the  change  produced  in  the 
curves  connecting  P.D.  and  current  for  a  given  length  of  arc, 
when  a  solid  positive  carbon  was  substituted  for  a  cored  one  of 
the  same  diameter,  the  negative  carbons  in  both  cases  being 
solid. 

These  curves  connect  P.D.  with  current  for  a  silent  arc  of 
4mm.,  A  A  A  when  both  carbons  were  solid,  B  B  B  when  the 
positive  was  cored,  the  positive  carbon  being  9mm.  and  the 
negative  8mm.  in  diameter  in  both  cases.  We  see  that  the 


SURFACE  OF  CRATER  AND  P.D.  133 

curve  with  a  cored  positive  carbon  is  from  three  to  six  volts 
lower  than  that  with  a  solid  positive.  This  diminution  of  P.D. 
with  a  cor«d  carbon  does  not  appear  to  be  uniform  whatever 
the  length  of  arc,  but  is  much  greater  with  short  arcs  than  with 
long  ones;  evidently  also  it  is,  on  the  whole,  greater  with 
smaller  currents  than  with  larger  ones. 

The  position  of  the  hissing  point  on  each  curve  differs 
according  as  a  cored  or  a  solid  positive  carbon  is  used,  as  may 
be  seen  by  comparing  Fig.  38  with  Figs.  39,  40,  &c.  The  reason 
of  this  will  be  discussed  in  the  chapter  on  hissing  arcs. 

The  two  most  important  points  of  difference  in  the  connection 
between  the  P.D.  and  the  current  for  a  silent  arc  of  fixed  length 
are,  then — 

(1)  With  a  solid  carbon  the  P.D.  continually  diminishes  as 
the  current  increases ;    with  a  cored,  carbon  the  P.D.  either 
diminishes    much  less  than  with  a  solid  carbon,  or  remains 
constant  for  all   currents    above   a  given  value,   or   actually 
increases  with  the  current  after  falling  to  a  minimum. 

(2)  The  P.D.  is  in  all  cases  lower  with  the  cored  than  with 
the  solid  carbon. 

This  second  variation  probably  depends  upon  the  greater 
ease  with  which  the  softer  carbon  is  volatilised ;  the  first  is  an 
apparently  complicated  effect,  the  explanation  of  which  becomes 
perfectly  simple,  however,  on  the  hypothesis  that  with  a  given 
negative  carbon  the  P.D.  required  to  send  a  given  current  through 
a  fixed  length  of  arc  depends  principally,  if  not  entirety,  on  the 
nature  of  the  surface  of  the  crater,  being  greater  or  less  according 
as  the  carbon  of  which  that  surface  is  composed  is  harder  or  softer. 

This  is  tantamount  to  saying  that  the  only  part  of  the  positive 
carbon  that  exerts  much  influence  over  the  P.D.  between  the 
carbons  is  that  which  forms  the  surface  of  the  crater. 

Consider,  now,  the  nature  of  the  surface  of  the  crater  of  a 
cored  positive  carbon  when  the  length  of  the  arc  is  fixed,  but 
the  current  may  be  varied.  While  the  current  is  very  small 
the  area  of  the  crater  will  be  less  than  that  of  the  core,  and  its 
surface  will  therefore  be  composed  entirely  of  soft  carbon. 
Hence,  by  the  above  hypothesis,  the  P.D.  for  each  current  will 
be  much  the  same  as  if  the  whole  carbon  were  soft  like  the  core. 
Thus,  until  the  current  is  so  large  that  the  crater  exactly  covers 
the  core,  the  curve  connecting  P.D.  and  current  for  a  fixed 


134 


THE  ELECTEIG  ARC. 


length  of  arc  will  be  practically  the  same  as  if  the  whole  positive 
carbon  were  as  soft  as  the  core. 

When  the  crater  extends  further  than  the  core,  however,  part 
of  its  surface  will  be  formed  of  the  hard  outer  carbon,  and,  by 
the  hypothesis,  the  P.D.  between  the  carbons  will  then  be 
higher  than  it  would  be  if  the  whole  surface  of  the  crater  were 
of  soft  carbon.  Hence,  after  this  point  is  reached,  the  curve 
connecting  P.D.  and  current  for  a  fixed  length  of  arc  will  no 
longer  be  the  same  as  if  the  whole  positive  carbon  were  soft, 
but  will  diverge  from  that  curve,  the  distance  between  the  two 
becoming  greater  as  the  current,  and  therefore  the  area  of  the 
crater,  increases.  For,  after  it  has  once  covered  the  core,  any 


Current  in  Amperes. 

ABC,  Carbons :   Positive  solid,  but  soft  as  a  core  ;   negative  solid  and 
hard.     A  B  D  E,  Carbons  :  Positive  cored  ;  negative  solid  and  hard. 

FIG.  43.— Ideal  Curves  of  P.D.  and  Current  for  Constant  Length  of  Arc. 

addition  to  the  area  of  the  crater  must  be  an  addition  to  the 
hard  carbon  part,  hence  the  ratio  of  hard  carbon  to  the  total 
amount  of  carbon  in  this  surface  must  continually  increase. 

Fig.  43  gives  a  rough  idea  of  the  two  curves  connecting  the 
P.D.  between  the  carbons  with  the  current  for  a  fixed  length 
of  arc — A  B  C  with  the  positive  carbon  uncored  but  as  soft  as 
a  core,  A  B  D  E  with  it  cored,  the  negative  carbon  being  solid* 
and  the  same  in  both  cases. 


SURFACE  OF  CEATEE  AND  P.D.  135 

The  two  curves  coincide  up  to  the  point  B,  at  which  the 
crater  exactly  covered  the  core.  After  this  point  was  reached 
the  crater  began  to  cover  some  of  the  hard  carbon ;  the  P.D. 
was  therefore  greater  with  the  cored  than  with  the  uncored 
carbon,  but  it  still  diminished  as  the  current  increased,  though 
more  and  more  slowly.  At  last  the  tendency  for  the  P.D.  to 
fall,  caused  by  the  increase  of  the  current,  was  entirely  counter- 
balanced by  the  tendency  to  rise,  caused  by  the  increasing 
amount  of  hard  carbon  covered  by  the  crater.  At  this  point 
(D  on  the  curve)  the  P.D.  became  a  minimum,  and  as  the 
current  was  further  increased  the  P.D.  slowly  rose  till  E,  the 
hissing  point,  was  reached. 

It  is  obvious  that  the  position  of  the  point  B  must  be  deter- 
mined by  the  area  of  the  cross  section  of  the  core :  the  larger 
this  cross  section,  the  larger  the  crater  can  be  without  touching 
the  hard  carbon,  and  consequently  the  greater  will  be  the 
current  that  can  flow  before  the  crater  will  exactly  cover  the 
core. 

The  position  of  D,  the  point  of  minimum  P.D.  with  a 
cored  positive  carbon,  has  been  shown  to  depend  upon  the 
length  of  the  arc,  and  apparently  also  on  the  diameters  of  the 
carbons  (p.  131).  As  a  matter  of  fact,  however,  it  is  not  so 
much  upon  the  diameters  of  the  carbons  that  it  depends  as 
upon  the  diameter  of  the  positive  carbon  compared  with 
the  diameter  of  its  core.  For,  evidently,  if  the  cross  section 
of  the  core  were  very  large  compared  with  the  cross  section 
of  the  whole  carbon,  so  that  the  outer  hard  carbon  was  a 
mere  shell,  the  current  would  be  so  large  before  the  crater 
touched  the  hard  carbon  at  all,  that  hissing  would  take  place 
before  the  minimum  P.D.  had  been  reached.  With  a  smaller 
core,  the  diameter  of  the  carbon  still  remaining  the  same, 
the  point  of  minimum  P.D.  and  the  hissing  point  might 
coincide,  while  with  a  still  thinner  core  the  minimum  P.D. 
would  be  reached  before  hissing  began,  as  in  the  curves  in 
Fig.  41.  Thus  the  minimum  P.D.  for  any  given  length  of  arc 
with  a  cored  positive  carbon  of  given  diameter  might  be  made 
to  correspond  with  any  current  we  chose  by  making  the  cross 
section  of  the  core  of  a  suitable  size.  The  position  of  D  must 
also  depend  upon  the  degree  of  hardness  of  the  outer  shell. 
For  the  harder  this  is,  the  greater  will  be  the  P.D.  with  any 


136 


THE  ELECTEIC  ARC. 


given  proportion  of  hard  carbon  in  the  surface  of  the  crater ; 
therefore,  all  other  things  being  equal,  D  will  correspond  with 
a  smaller  current  the  harder  the  outer  cylinder  of  the  carbon. 
An  interesting  point  that  follows  from  the  particular  form 
of  the  curves  in  Figs.  40  and  41  is  that  with  a  cored  positive 
carbon  certain  P.Ds.  will  send  two  distinct  currents  through 
the  arc.  For  example,  a  P.D.  of  42  volts  (Fig.  40)  will  send 
a  current  of  either  3  or  21  amperes  through  a  1mm.  arc.  This 
points  to  the  complete  equation  connecting  P.D.  current,  and 
length  of  arc  for  silent  arcs  produced  with  a  cored  positive  and 
a  solid  negative  carbon,  'being  a  quadratic  in  terms  of  A,  the 
current  flowing. 


35 

1234567 

Length  of  Arc  in  Millimetres. 

FIG.  44.  —  P.D.  and  Length  of  Arc  for  Various  Constant  Currents. 
Carbons  :  Positive,  llmm.,  solid  ;  negative,  9min.,  solid. 

The  curves  connecting  the  steady  P.D.  between  the  carbons 
with  the  current  flowing  for  certain  constant  lengths  of  arc 
having  been  discussed,  it  is  now  proposed  to  examine  the 
connection  between  the  steady  P.D.  and  the  length  of  the  arc 
with  certain  constant  currents. 

The  curves  in  Fig.  44,  showing  this  connection  when  two  solid 
carbons  were  used — the  positive  llmm.  and  the  negative  9mm. 
in  diameter — were  obtained,  not  from  the  numbers  given  in 
Table  XII.,  but  from  the  curves  in  Fig.  38,  plotted  with  those 


CONSTANT  CURRENTS.  137 

numbers.  The  ordinates  are  the  P.Ds.  between  the  carbons 
and  the  abscissae  the  lengths  of  the  arc,  the  current  being  a 
constant  for  each  curve.  The  result  is  a  series  of  straight  lines 
making  a  smaller  angle  with  the  axis  of  length  the  larger  the 
value  of  the  constant  current  flowing.  These  lines  all  meet  at 
one  point,  which  is  to  the  left  of  the  axis  of  P.D.,  show- 
ing that  it  corresponds  with  a  negative  length  of  arc,  but 
above  the  axis  of  length  of  arc,  and  therefore  indicating 
a  positive  P.D.  This  point  shows,  of  course,  the  length 
of  arc  for  which  the  P.D.  is  constant,  whatever  the  current 
flowing.  That  this  length  is  negative  implies  no  absurdity, 
for  our  definition  of  the  length  of  the  arc  is  the  perpendicular 
distance  between  the  extreme  tip  of  the  negative  carbon  and 
the  plane  through  the  edge  of  the  crater.  If  there  were  a  deep 
crater,  and  the  point  of  the  negative  carbon  were  thrust  into  it, 
the  distance  between  that  point  and  the  edge  of  the  crater  would 
have  to  be  measured  in  a  direction  opposite  from  that  in  which 
it  was  measured  when  the  point  of  the  negative  carbon  was 
outside  the  crater.  Hence  a  negative  sign  must  be  given  to 
the  length  of  the  arc  when  the  tip  of  the  negative  carbon  is 
inside  the  crater. 

As  a  matter  of  fact,  however,  I  have  never  succeeded  in 
getting  a  permanently  silent  arc  with  the  tip  of  the  negative 
carbon  inside  the  crater,  however  small  a  current  was  used,  and 
since  all  the  conditions  change  as  soon  as  the  arc  begins  to  hiss, 
the  point  at  which  all  the  lines  in  Fig.  44  meet  must  be  con- 
sidered as  simply  an  ideal  point,  at  which  all  the  lines  ivoidd 
meet  if  the  conditions  remained  the  same  when  the  arc  was 
very  short,  or  even  negative,  as  they  were  when  the  arc  was 
1mm.  long  and  more.  Thus,  with  loth  carbons  solid  there  is  no 
real  length  of  arc  ivith  which  the  P.D.  is  constant  for  all  cur- 
rents, a  fact  which  has  already  been  deduced  from  the  curves 
in  Fig.  38. 

The  lines  in  Fig.  44  being  straight  shows  that,  with  a  con- 
stant current,  a  fixed  change  in  the  length  of  the  arc  involves 
a  fixed  change  in  the  P.D.  between  the  carbons.  For  instance, 
with  a  constant  current  of  5  amperes,  a  change  of  length  from 
1mm.  to  2mm.  is  accompanied  by  a  change  of  P.D.  from  45'4 
to  49-6  volts,  that  is  4-2  volts;  and  a  change  of  length  from 
6tnm.  to  7mm.  is  accompanied  by  a  change  of  P.D.  from  65 -9 


138  THE  ELECTRIC  ARC. 

to  70-1  volts,  or  4'2  volts.  With  a  constant  current  of  another 
value,  however,  the  change  in  the  P.D.  for  the  same  amount  of 
change  in  the  length  of  the  arc  would  be  different,  being 
greater  for  a  smaller  current  and  less  for  a  larger  one,  as  is 
shown  by  the  lines  in  Fig.  44  making  smaller  angles  with  the 
axis  of  length  the  larger  the  current.  Thus,  with  a  current  of 
14  amperes,  the  constant  change  of  P.D.  for  a  change  of  1  mm. 
in  the  length  of  the  arc  is  about  2-8  volts.  Hence  ivith  solid 
carbons  a  given  increase  in  the  length  of  the  arc  involves  an 
increase  in  the  P.D.  between  the  carbons  which  is  constant  for  a 
constant  current,  but  ivhich  diminishes  as  the  value  of  the  constant 
current  increases. 

The  fact  that  with  solid  carbons  a  linear  law  connects  the 
P.D.  between  the  carbons  with  the  length  of  the  arc  for  con- 
stant currents  follows  directly  from  Edlund's  straight  line  law 
connecting  the  apparent  resistance  of  the  arc  with  its  length 
for  constant  currents  (see  p.  34).  For  if  we  put  Edlund's  law 

in  the  form 

v 

-L-a  +  W, 

A 

it  is  quite  evident  that,  when  A  is  constant, 


or 

follows  directly  from  it.  The  discovery  of  this  law  is  generally 
attributed  to  Frolich,  but,  so  far  from  discovering  it,  Frolich 
missed  the  whole  point  of  Edlund's  work,  and  did  not  see  that 
a  and  6  in  the  first  equation  and  m  and  n  in  the  last  varied 
with  each  current  that  was  employed. 

If  in  the  last  equation  we  make  I  equal  to  0,  we  have 

V  =  m, 

an  equation  which  has  given  rise  to  the  idea  of  the  existence 
of  a  constant  back  E.M.F.  in  the  arc.  But  in  this  equation  m 
is  only  constant  for  one  current,  and  diminishes  as  the  current 
increases,  as  may  be  seen  by  a  comparison  of  the  points  for 
which  1  =  0  in  Fig.  44.  For  instance,  the  P.D.  is  about 
39'8  volts  for  a  current  of  14  amperes,  41  -2  volts  for  one  of 
5  amperes,  and  so  on.  It  may  be  contended  that  if  the  depth 
of  the  crater  were  taken  into  account  in  the  length  of  the  arc, 
in  which  case  length  of  arc  0  would  really  mean  that  there 
was  no  distance  between  the  positive  and  negative  carbons,  the 


CONSTANT  CURRENTS. 


139 


P.D.  might  really  be  constant  for  all  currents  with  length  of 
arc  0 ;  but  Peukert,  who  used  two  solid  carbons,  and  who 
took  his  measurements  before  a  crater  had  had  time  to  form, 
by  filing  the  carbons  flat  before  each  experiment,  obtained 
lines  very  like  those  in  Fig.  44,  and  found  also  that  the  P.D. 
for  length  of  arc  0  diminished  as  the  current  increased. 

The  curves  connecting  P.D.  and  length  of  arc  for  constant 
currents  are  by  110  means  so  simple  when  a  cored  positive 
carbon  is  used  as  when  both  carbons  are  solid,  as  may  be 
seen  from  the  curves  in  Figs.  45,  46  and  47.  To  begin 
with,  none  of  them  are  straight  lines,  although  as  the  value  of 
the  constant  current  increases  they  approximate  more  and  more 
closely  to  straight  lines.  This  divergence  from  the  straight 


GU 


012  45 

Length  of  Arc  in  Millimetres. 

FIG.  45. — P.D.   and  Length  of  Arc  for  Various  Constant  Currents. 
Carbons  :  Positive,  18mm.,  cored  ;  negative,  15mm.,  solid. 

line  law  shows  that  with  a  constant  current  the  influence  of  the 
core  is  greatest  with  the  shortest  arc,  and  becomes  less  as  the 
arc  increases  in  length,  for  otherwise  the  lowering  of  the  P.D. 
would  be  exactly  the  same  for  each  length  of  arc,  and  the 
curves  for  solid  and  cored  carbons  would  be  at  a  constant 
distance  from  one  another.  That  this  is  not  so  is  apparent  even 
in  the  curves  for  constant  lengths  of  arc  (Figs.  39,  40  and  41). 
Take,  for  instance,  the  curves  for  arcs  of  1mm.,  2mm.  and 
3mm.  in  Fig.  39.  With  a  current  of  10  amperes  the  distance 
between  the  first  two  curves  is  about  twice  as  great  as  the 
distance  between  the  second  and  third.  But  in  Fig.  38,  for 


140 


THE  ELECTRIC  ARC. 


solid  carbons,  the  distances  between  the  two  sets  of  points  are 
the  same.  For  large  currents  the  distances  are  much  more 
nearly  equal,  and  that  is  why  the  curves  in  Figs.  45,  46  and  47 
are  so  much  nearer  to  straight  lines  for  large  currents  than  for 
small  ones. 


4  5  67 

Length  of  Arc  in  Millimetres. 

FIG.  45. — P.D.  and  Length  of  Arc  for  Various  Constant  Currents. 
Carbons  :  Positive,  13mm.,  cored  ;  negative,  llmm.,  solid. 


1234567 
Length  of  Arc  in  Millimetres. 

FIG.  47.— P.D.  and  Length  of  Arc  for  Various  Constant  Currents. 
Carbons :  Positive,  9mm.,  cored  ;  negative,  8mm.,  solid. 


CONSTANT  CUBKENTS.  141 

We  have  seen  that  when  both  carbons  are  solid  there  is  no 
positive  length  of  silent  arc,  for  which  the  P.D.  is  independent 
of  the  current,  but  with  a  cored  positive  carbon  this  is  other- 
wise. Owing  to  the  fact  that  the  P.D.  is  most  changed  by  the 
core  with  small  currents  and  short  arcs,  the  curve  connecting 
P.D.  and  length  of  arc  for  the  smallest  current  bends  down 
the  most  towards  the  axis  of  length,  and  the  other  curves  bend 
less  and  less  as  the  current  increases,  so  that  the  curves  all 
cross  one  another  to  the  right  of  the  axis  of  P.D.,  instead  of 
meeting  at  a  point  to  the  left,  as  they  do  with  solid  carbons. 
The  curves  do  not  actually  cut  one  another  at  the  same  point,, 
but  at  points  which  are  very  near  together  for  all  but  the 
smallest  currents,  and  the  region  in  which  these  points  are  is,, 
of  course,  the  region  in  which  Mr.  Schwendler's  observation  is 
true  that  the  P.D.  is  practically  independent  of  the  current 
(see  page  132),  for  in  this  region,  with  a  given  length  of  arc, 
there  is  the  same  P.D.  between  the  carbons  whatever  current 
is  flowing. 

The  particular  length  of  silent  arc  for  which  the  P.D.  is 
practically  independent  of  the  current  is  best  seen  from  the 
points  of  intersection  of  the  curves  in  Figs.  45,  46  and  47. 
This  length  is  evidently  a  little  under  2mm.  When  both 
the  positive  and  negative  carbons  are  cored  the  point  at  which 
the  curves  connecting  P.D.  and  length  of  arc  for  different 
currents  cut  one  another  becomes  very  marked  (Fig.  48),. 
and  the  length  of  arc  corresponding  with  this  intersecting 
point  diminishes  to  0'75mm.  If  the  curves  corresponding 
with  those  in  Figs.  39,  40  and  41  had  been  drawn  for 
these  carbons,  the  point  for  3  amperes  would  have  been 
found  to  be  on  the  first  steep  part  of  the  curve  for  each 
length  of  arc.  Hence  the  high  position  of  the  3-ampere 
curve  in  Fig.  48. 

One  result  of  this  crossing  of  the  curves  in  Figs.  45,  46 
and  47  is  very  interesting,  and  it  is  seen  particularly  well  in 
Figs.  46  and  47.  Instead  of  the  P.D.  for  length  of  arc  0  diminish- 
ing as  the  current  increases,  as  it  has  been  shown  to  do  with 
solid  carbons,  it  increases  with  the  current.    This  fact  was  first 
observed  by  Nebel  in  1886,  but  at  that  time  the  differences- 
occasioned  by  the  use  of  cored  instead  of  solid  positive  carbons- 
were  not  understood,  and  he  did  not,  therefore,  realise  that 


142 


THE  ELECTRIC  ARC. 


this  increase  of  the  P.D.  for  length  of  arc  0,  with  increase  of 
current,  depended  on  the  use  of  a  cored  positive  carbon. 

The  likenesses  and  differences  between  the  curves  in  Fig.  44 
for  solid  carbons,  and  those  in  Figs.  45,  46  and  47,  for  which  a 
cored  positive  carbon  was  used,  may  be  summed  up  in  the 
following  way : — 

With  a  Constant  Current. 
LIKENESSES. 

(1)  The  P.D.  increases  as  the  length  of  the  arc  increases. 

(2)  The  P.D.  increases  less  for  a  given  increase  in  the  length 
of  the  arc  the  larger  the  value  of  the  constant  current  that  is 
flowing. 


65  i — 


0123456 
Length  of  Arc  in  Millimetres. 

FIG.  48. — P.D.  and  Length  of  Arc  for  Various  Constant  Currents. 
Carbons :  Positive,  18mm.,  cored  ;  negative,  15mm.,  cored. 

DIFFERENCES. 

(1)  The  P.D.  is  always  higher  with  solid  carbons  than  with 
a  cored  positive  carbon,  but  the  difference  between  the  two 
diminishes  as  the  arc  increases  in  length. 

(2)  The  rate  of  change  of  P.D.  with  change  of  length  is 
constant  with  solid  carbons,  but  diminishes  as  the  length  of  the 
arc  increases  with  a  cored  positive  carbon. 

(3)  This   rate   of   change   with   a   cored   positive   becomes 
smaller  and  more  nearly  constant  for  all  lengths  of  arc  as  the 
value  of  the  constant  current  increases. 

(4)  The  P.D.  corresponding  with  length  of  arc  0  diminishes 


SURFACE  OF  CEATEE  AND  P.D.  143 

AS  the  current  increases  with  solid  carbons,  but  increases  with 
the  current  with  a  cored  positive  carbon. 

These  differences  have  now  to  be  explained. 

When  it  was  found  above  that  the  law  of  the  relation  between 
the  P.D.  and  the  current  with  constant  length  of  arc  varied 
according  as  the  positive  carbon  was  solid  or  cored,  it  was  shown 
that  this  variation  could  be  reasonably  explained  on  the  hypo- 
thesis that  with  a  given  negative  carbon  the  P.D.  required  to  send 
a  given  current  through  a  -fixed  length  of  arc  depends  principally, 
if  not  entirely,  on  the  nature  of  the  surface  of  the  crater,  being 
greater  or  less  according  as  the  carbon  of  which  this  surface  is 
composed  is  harder  or  softer. 

If  this  hypothesis  be  true,  it  should  explain  all  the  changes 
in  the  laws  connecting  P.D.,  current  and  length  of  arc  when 
a  cored  instead  of  a  solid  positive  carbon  is  used,  which- 
ever one  of  the  three  variables  we  may  choose  to  consider 
as  constant.  Therefore,  it  should  explain  the  differences 
between  the  curves  in  Fig.  44  and  those  in  Figs.  45,  46  and 
47.  We  will  see  how  far  it  does  so. 

Let  A  P  Q  R  (Fig.  49)  be  the  straight  line  representing  the 
connection  between  the  P.D.  between  the  carbons  and  the 
length  of  the  arc,  with  a  given  current  flowing,  when  both 
carbons  are  solid,  and  let  A'  P'  Q'  R'  be  the  curve  representing 
the  same  connection  when  the  positive  carbon  has  a  soft  core. 
Let  P,  Q  and  R  be  the  points  on  the  upper  line  for  arcs  of 
1mm.,  2mm.  and  3mm.  respectively,  and  let  P',  Q'  and  R' 
be  the  corresponding  points  on  the  lower  curve.  Then  P  P', 
Q  Q'  and  R  R',  represent  the  diminution  in  the  P.D.  caused  by 
the  soft  core  when  the  arcs  are  1mm.,  2mm.  and  3mm.  respec- 
tively, with  the  given  current  flowing.  According  to  the  above 
hypothesis,  this  diminution  depends  on  how  much  of  the  carbon 
in  the  surface  of  the  crater  is  soft ;  thus  PP',  Q  Q'  and  RR'  may 
be  taken  to  represent  the  different  proportions  of  soft  carbon 
in  the  surface  of  the  crater  with  the  different  lengths  of  arc. 
If  the  proportion  is  great  the  diminution  of  P.D.  is  great, 
if  small  it  is  small.  Hence,  since  experiment  shows  that 
P  P'  is  greater  than  Q  Q',  and  Q  Q'  than  R  R',  we  must 
conclude  that  the  proportion  of  soft  carbon  in  the  surface  of  the 
crater  diminishes  as  the  length  of  the  arc  increases  with  a  constant 
current  flowing.  Now  the  only  way  in  which  the  proportion  of 


144 


ELECTRIC  ARC. 


soft  carbon  m  the  surface  of  the  crater  can  change  is  by 
different  amounts  of  hard  carbon  being  added  to  it,  for  as  long 
as  the  area  of  the  crater  is  less  than  that  of  the  core  the 
proportion  of  soft  carbon  is  a  constant,  namely,  the  whole, 
and  as  soon  as  the  crater  covers  the  core  the  amount  of  soft 
carbon  is  a  constant,  but  the  amount  of  hard  carbon  can 
change  by  the  enlargement  of  the  area  of  the  crater;  hence 
the  proportion  of  soft  carbon  in  the  crater  becomes  less  as 
the  crater  enlarges  itself,  for  more  and  more  hard  carbon  is 
added,  and  the  soft  carbon  remains  the  same.  But  we  have 
seen  that  by  the  hypothesis  the  proportion  of  soft  carbon  in 
the  surface  of  the  crater  must  diminish  as  the  arc  increases 


s  in 

S 


S 


0128^ 

Length  of  Arc  in  Millimetres. 

FIG.  49. 

in  length  with  a  constant  current,  therefore,  since  the  only 
way  in  which  this  can  happen  is  by  the  area  of  the  crater 
becoming  enlarged,  it  follows  that,  if  the  hypothesis  is  correct, 
the  area  of  the  crater  must  increase  as  the  length  of  the  arc 
increases,  when  a  cored  positive  carbon  is  used  and  a  constant 
current  is  flowing. 

Before  proceeding  further  it  will  be  well  to  define  accurately 
what  is  meant  by  the  expressions  "area  of  crater,"  "pro- 
portion of  soft  carbon  in  the  surface  of  the  crater."  It  must 
be  clearly  understood  that,  for  the  present,  the  depth  of  the 
crater  has  been  and  will  be  left  entirely  out  of  account,  for  the 


CRATER  RATIOS.  145 

results  of  experiments  show  that  perfectly  clear  and  definite 
laws  can  be  obtained  without  considering  it,  and  the  probability 
is  therefore  that  it  has  very  little  effect  on  the  action  of  the 
arc.  By  the  term  area  of  the  crater,  then,  we  mean  the  area  of 
the  mouth  of  the  crater,  or,  still  more  accurately,  the  plane  area 
of  that  region  of  the  end  of  the  positive  carbon  which  is  sharply 
cut  off  from  the  rest  by  its  peculiar  brilliance  and  whiteness. 
The  area  of  the  soft  carbon  in  the  surface  of  the  crater  is  taken 
to  be  the  projection  on  the  mouth  of  the  crater  of  that  area  of 
the  crater  that  is  composed  of  soft  carbon,  and  the  proportion 
of  soft  carbon  in  the  surface  of  the  crater  is  measured  by  the 
ratio  of  the  area  of  the  soft  carbon  to  tlie  total  area  of  the 
crater.  This  ratio  for  each  current  and  length  of  arc  we  shall 
call  its  "  soft  crater  ratio"  while  the  ratio  of  the  amount  of 
hard  carbon  to  the  total  amount  of  carbon  in  the  surface  of 
the  crater  will  be  called  the  "  hard  crater  ratio" 

It  has  been  shown  that  of  the  "differences"  mentioned  on 
page  142  the  first  must  arise,  according  to  hypothesis,  from 
the  area  of  the  crater  increasing  as  the  length  of  the  arc 
increases.  To  see  the  meaning  of  the  second  we  must  turn 
again  to  Fig.  49.  In  this  figure  Q'  N',  R'  M'  represent  the 
increase  of  P.D.  accompanying  a  change  of  1mm.  in  the  length 
of  the  arc  when  the  positive  carbon  is  cored,  the  first  from 
1mm.  to  2mm.  and  the  second  from  2mm.  to  3mm.  The 
accompanying  changes  in  the  soft  crater  ratios  are  represented 
by  N  P'  and  M  Q'.  For,  since  R'  M  and  Q'  N  are  both  parallel 
to  APQR,  PP'-QQ'  =  NP'  and  QQ'-RR'  =  M  Qr,  and 
P  P',  QQ'  and  RR'  have  been  shown  to  represent  the  soft  crater 
ratios  for  arcs  of  1mm.,  2mm.  and  3mm.  respectively.  Now 
difference  (2)  (p.  142)  says  that  the  change  of  P.D.  with  change 
of  length  with  a  cored  positive  carbon  diminishes  as  the 
length  of  the  arc  increases;  that  is  to  say,  we  know  from 
experiment  that  R'  M'  is  less  than  Q'  N'  (Fig.  49).  We  can 
easily  see  what  this  must  mean  in  crater  ratios  according  to 
our  hypothesis.  We  have 


and,  since  K'M'<Q'N', 

/.  SQ'<TP'. 
That  Is  SM  +  MQ'<TN  +  NP'. 


146  THE  ELECTRIC  AEG. 

But  S  R'  M  and  T  Q'  N  are  equal  triangles, 

/.  SM  =  TN, 

.'.  MQ'<NP'. 

But  M  Q',  N  P'  are  the  changes  of  soft  crater  ratio  accompany- 
ing changes  in  the  length  of  the  arc  as  that  length  is  increased 
by  equal  increments.  Hence  it  has  been  shown  that,  since  the 
change  of  P.D.  with  change  of  length  diminishes  as  the  arc 
increases  in  length,  it  follows,  if  our  hypothesis  be  correct, 
that  the  rate  of  change  of  soft  crater  ratio  with  change  of  length 
must  also  diminish  as  the  arc  increases  in  length.  In  other 
words,  we  have  that 

(2)  When  a  cored  positive  carbon  is  used,  and  a  constant  current 
is  flowing,  the  rate  of  the  change  that  takes  place  ivith  change  of 
length  in  the  ratio  of  the  soft  carbon  to  the  total  amount  of  carbon 
in  the  surface  of  the  crater  must  diminish  as  the  arc  increases  in 
length. 

Difference  (3)  translated  into  crater  ratios  evidently  means  that 
the  rate  of  change  of  soft  crater  ratio  with  change  of  length  is 
smaller  and  becomes  more  nearly  equal  for  all  lengths  of  arc  as 
the  value  of  the  constant  current  increases  ;  or, 

(3)  When  a  cored  positive  carbon  is  used  the  rate  of  the  change 
that  takes  place  with  change  of  length  in  the  ratio  of  the  soft 
carbon  to  the  total  amount  of  carbon  in  the  surface  of  the  crater 
is  smaller  and  becomes  more  nearly  equal  for  all  lengths  of  arc 
as  the  value  of  the  constant  current  increases. 

Difference  (4)  can  hardly  be  called  a  separate  phenomenon, 
for  not  only  with  length  of  arc  0,  but  also  with  lengths  of  arc 
1mm.  and  2mm.,  the  P.D.  increases  with  the  current  with  the 
cored  positive  carbons  used  for  these  experiments  (see  Figs.  45, 46 
and  47),  but  the  increase  with  length  of  arc  0  has  so  important 
a  bearing  on  the  question  of  a  back  E.M.F.  in  the  arc  that  it  is 
quite  necessary  to  show  that  this  increase  is,  so  to  say,  accidental, 
and  depends  merely  on  the  presence  of  the  core  in  the  positive 
carbon.  This  increase  has  already  been  explained  above, 
as  being  due  to  the  rise  of  P.D.,  caused  by  the  greater  amount 
of  hard  carbon  in  the  surface  of  the  crater  with  a  larger  current 
more  than  counterbalancing  the  fall  due  to  the  increase  of  the 
current.  In  other  words,  with  short  arcs  the  rise  of  P.D.  due 
bo  the  diminution  of  soft  crater  ratio  with  an  increase  of 
current  more  than  counterbalances  the  fall  of  P.D.  due  to  that 
increase  of  current. 


SUMMARY.  147 

One  more  point  must  still  be  mentioned  with  regard  to  the 
curves  in  Figs.  45,  46  and  47,  before  proceeding  to  justify  the 
hypothesis  upon  which  the  explanation  of  the  difference  between 
the  arc  curves  for  solid  and  cored  positive  carbons  rests,  by  an 
examination  of  the  curves  connecting  the  area  of  the  crater 
with  the  other  variables  of  the  arc.  The  curves  for  6  amperes 
in  Fig.  45  and  for  5  amperes  in  Fig.  46  change  their  curvature 
completely  for  arcs  between  0  and  1mm.  This  change  can  only 
be  caused  by  the  complete  absence  of  hard  carbon  in  the  surface 
of  the  crater,  so  that  those  portions  of  the  curve  really  belong 
to  the  straight  lines  that  connect  P.D.  and  length  of  arc  for  a 
solid  soft  positive  carbon  and  a  hard  negative  carbon.  Those 
portions  of  the  curves,  in  fact,  are  the  portions  for  which  the 
crater  is  so  small  that  it  is  entirely  in  the  core.  With  the 
smaller  sized  carbons  the  core  is  smaller,  and  with  a  current  of 
4  amperes  the  crater  was  not  small  enough  with  the  9  mm. 
cored  positive  carbon  to  consist  entirely  of  soft  carbon;  therefore 
there  is  no  such  change  in  the  curve  in  Fig.  47. 


SUMMARY. 

THE  STEADY  P.D.  BETWEEN  THE  CARBONS  WHEN  THE  LENGTH  OF 
THE  ARC  is  FIXED  AND  THE  CURRENT  VARIED. 

With  Both  Carbons  Solid* 

I.  With  the  smallest  current  the  P.D.  is  the  highest ;  as 
the  current  is  increased  the  P.D.  falls,  rapidly  at  first,  and 
then  more  and  more  slowly,  until  the  hissing  point  is  reached ., 

II.  With  a  given  range  of  current,  the  P.D.  changes  much 
more  with  a  long  arc  than  with  a  short  one. 

III.  From  I.  and  II.  it  follows  that  the  ratio  of  change  of 
P.D.  to  change  of  current  is  greater  the  smaller  the  current 
and  the  longer  the  arc. 

With  the  Positive   Carbon  either   Cored  or  Solid,  and  the 
Negative  Carbon  Solid. 

IV.  With  any  given  P.D.  the  longer  the  arc  the  larger  is 
the  current,  and  consequently 

V.  With  a  given  P.D.  the  longer  the  arc  the  smaller  is  its 
apparent  resistance. 

L2 


148  THE  ELECTRIC  AEG. 

With  the  Positive  Carbon  Cored  and  the  Negative  Carbon  Solid. 

VI.  The  curves  connecting  the  P.D.  between  the  carbons 
with  the  current  for  a  fixed  length  of  arc  vary  in  form  accord- 
ing to  the  ratio  that  the  diameter  of  the  core  of  the  positive 
carbon  bears  to  the  whole  diameter  of  the  carbon.     When  the 
carbons  are   such  as  are  ordinarily  used  for  electric  lighting 
purposes,  the  P.D.  generally  falls  to  a  minimum  as  the  current 
is  increased,  and  then  rises  again  as  the  current  is  still  further 
increased,  till  hissing  takes  place. 

VII.  With  the  same   pair  of  carbons  the  minimum  P.D. 
corresponds  with  a  larger  current  the  longer  the  arc. 

VIII.  With  arcs  of  from  4  to  7mm.  with  the  larger  sizes  of 
carbons,  as  the  current  is  increased  above  a  certain  value,  the 
P.D.,  as  it  falls  to  a  minimum  and  then  rises,  changes  sa 
slightly  that  it  may  be  considered  practically  constant  for  a 
wide  range  of  current. 

IX.  The  P.D.   is  always  lower  for  any  given  current  and 
length  of  arc  when  a  cored  positive  carbon  is  used  than  with  a 
hard  solid  positive  carbon. 

THE  STEADY  P.D.  BETWEEN  THE  CARBONS  WHEN  THE  CURRENT  is 
FIXED  AND  THE  LENGTH  OF  THE  ARC  is  VARIED. 

With  both  Carbons  Solid. 

I.  A  straight  line  law  connects  the  P.D.  between  the  carbons 
with  the  length  of  the  arc,  and  hence  the  rate  of  change  of 
P.D.  with  change  of  length  is  a  constant  for  each  current. 

II.  The  straight  lines   meet  at  a  point  to  the  left  of  the 
axis  of  P.D.  and  above  the  axis  of  length,  therefore  there  is 
no  real  length  of  arc  for  which  the  P.D.  is  constant  for  all 
currents. 

III.  The  straight  lines  make  a  smaller  angle  with  the  axis 
of  length  the  larger  the  current,  hence  the  P.D.  for  length  of 
arc  0  diminishes  as  the  current  increases. 

With  the  Positive  Carbon  either  Cored  or  Solid  and  the  Negative 
Carbon  Solid. 

IV.  The  P.D.  increases  as  the  length  of  the  arc  increases. 

V.  The  rate  of  change  of  P.D.  with  change  of  length  is 
smaller  the  larger  the  current. 


SUMMARY.  149 

With  the  Positive  Carbon  Cored  and  the  Negative  Carbon  Solid. 

VI.  The  P.D.  is  lower  than  with  a  solid  positive  carbon. 

VII.  The  rate  of   change  of  P.D.  with  change  of  length 
diminishes  as  the  length  of  the  arc  increases. 

VIII.  The  rate  of  change  of  P.D.  becomes  more  nearly  con- 
stant as  the  current  increases. 

IX.  The  P.D.  for  length  of  arc  0  increases  with  the  current. 
On  the  hypothesis  that,  with  a  given  negative  carbon  the  P.D. 

required  to  send  a  given  current  through  a  fixed  length  of  arc 
depends  principally,  if  not  entirely,  on  the  nature  of  the  surface 
of  the  crater,  being  greater  or  less  according  as  the  carbon  of  which 
this  surface  is  composed  is  harder  or  softer,  these  changes  show 
that — 

X.  The  area  of  the  crater  must  increase,  and  consequently 
the  soft  crater  ratio  must  diminish  as  the  length  of  the  arc  in- 
creases. 

XL  The  rate  of  change  of  soft  crater  ratio  with  change  of 
length  must  diminish  as  the  length  of  the  arc  increases. 

XII.  The  rate  of  change  of  soft  crater  ratio  with  change  of 
length  must  be  smaller  and  become  more  nearly  constant  the 
larger  the  current. 


CHAPTER  V. 


AREA  01?  CRATER.  CRATER  RATIOS.  INFLUENCE  OF  DIAMETER 
OF  CARBONS  ON  P.D.  BETWEEN  THEM  WITH  GIVEN  CURRENT 
AND  LENGTH  OF  ARC.  RESISTANCE  CURVES  WITH  CONSTANT 
CURRENTS.  CONSTANT  POTENTIAL  DIFFERENCE  CURVES. 

IF  we  accept  the  definition  of  the  area  of  the  crater  given  in 
Chapter  IV.,  it  is  clear  that  that  area  can  only  be  measured 
while  the  arc  is  burning,  for  when  the  arc  is  extinguished  we 
have  no  certain  means  of  determining  the  boundary  of  the 
white-hot  part  of  the  carbon.  Table  XVI.  gives  the  diameter 
of  the  crater  measured  in  this  way  and  the  square  of  the 
diameter  for  different  currents  and  lengths  of  arc.  To  measure 
the  diameter  of  the  crater,  strips  of  paper  were  placed  across 
the  enlarged  image  of  the  crater,  when  it  was  properly  formed 
with  a  given  current  and  length  of  arc,  and  marks  were  made 
with  a  very  fine  pencil  at  the  points  where  the  paper  out  the 
diameter  of  the  image  of  the  crater. 

Table  XVI. — Diameter  of  Crater,  Square  of  Diameter,  P.D.  and 

Current  for  Different  Lengths  of  Arc. 
Carbons:  Positive,  13mm.,  cored;  negative,  llmm.,  solid. 


"c  a 

l~l 

1  =  2 

1  =  3 

1  =  4 

2  £ 
II 

Dia. 
in 
mm. 

Sq.  of 
dia. 

P.D. 

in 
volts. 

Dia. 
in 
mm. 

Sq.  of 
dia. 

P.D. 
in 
volts. 

Dia. 
in 
mm. 

Sq.  of 
dia. 

P.D. 
in 

volts 

Dia. 
in 
mm. 

Sq.  of 
dia. 

P.D. 
in 

volts. 

4 

3-1 

9'6 

38-76 

3-8  1  14-4 

51-0 

3-55 

12-6 

56-0 

3-55 

12-6 

58'6 

7 

4-2 

17-641  38-0 

4-2 

17-64 

45-15 

4-2 

17-64 

49-0 

4-4 

19-36 

Ml 

10 

4-25  i  18-06 

38-6 

4-75 

22-56 

43-3 

46-8 

4-9 

24-0 

49-7 

1f» 

5-45  29-7 

39-8 

5-6 

31-36 

432 

5-35 

28-62 

45-2 

5-8 

33-64 

47-75 

20 

64 

40-96 

40-9 

6-4 

40-96 

43-3 

6-4 

40-96 

44-9 

6-6 

43-56 

46-6 

152  THE  ELECTRIC  ARC. 

Each  set  of  numbers  in  Table  XVI.,  and,  indeed,  in  all  such 
tables,  is  liable  to  three  sources  of  error,  quite  apart  from  all 
actual  errors  of  observation  : 

(1)  The  carbons  may  not  be  of  uniform  constitution  and 
density. 

(2)  They  may  not  have  been  burnt  long  enough  to  acquire 
their  characteristic  shape  for  each  current  and  length  of  arc. 

(3)  They  may  not  have  been  perfectly  in  line. 

Errors  of  the  first  and  second  kind  would  affect  the  reading 
of  the  P.D. ;  the  third  would  render  it  difficult,  if  not  impossible, 
to  measure  either  the  length  of  the  arc  or  the  diameter  of  the 
crater  accurately.  When  to  all  these  possible  errors  are  added 
those  arising  from  the  difficulty  of  keeping  either  the  length  of 
the  arc  or  the  current  absolutely  constant,  and  the  possibility 
of  measuring  some  sector  of  the  crater  other  than  its  diameter, 
as  well  as  the  possibility  of  the  actual  boundary  of  the  crater 
being  obscured,  it  will  be  seen  that,  even  if  both  the  ammeter 
and  the  voltmeter  employed  could  be  always  depended  on  to 
give  perfectly  accurate  readings  under  all  circumstances,  the 
difficulties  of  finding  the  laws  which  connect  variables  thus 
obtained  would  be  very  great. 

Each  new  variable  introduces  a  fresh  difficulty,  and  thus  the 
law  connecting  the  area  of  the  mouth  of  the  crater  with  the 
length  of  the  arc — which  really  requires  a  correct  measurement 
of  four  variables,  the  P.D.,  the  current,  the  length  of  the  arc 
and  the  diameter  of  tha  crater — is  harder  to  determine  than  the 
law  which  connects  the  P.D.,  the  current  and  the  length 
of  the  arc  only,  for  which  no  measurement  of  the  crater  is 
necessary. 

As,  in  consequence  of  this  difficulty,  the  numbers  in 
Table  XVI  were  too  irregular  to  allow  the  shape  of  the 
curves  connecting  the  area  of  the  crater  with  the  length  of 
the  arc  to  be  determined  with  any  certainty,  curves  con- 
necting the  area  of  the  crater  with  the  other  variables  of 
the  arc  were  made  in  turn,  to  see  if  any  of  these  were  more 
regular.  The  best  results  were  obtained  with  the  curves 
connecting  the  P.D.  between  the  carbons  for  each  length  of  arc 
with  the  square  of  the  diameter  of  the  crater  for  the  same  length, 
when  the  current  was  constant  for  all  the  four  lengths  of  arc  in 
each  case.  These  curves  are  given  in  Fig.  50,  the  lines  having 


AREA  OF  CRATER. 


163 


been  drawn  as  nearly  as  possible  through  the  average  position  of 
the  points.  It  is  evident  that  they  are  straight  lines,  becoming 
more  steep  as  the  constant  current  increases.  From  the  values 
taken  from  these  curves  the  curves  in  Fig.  54(p.l59)  were  plotted 
connecting  the  current  with  the  area  of  the  crater  for  constant 
lengths  of  arc.  These  lines,  which  are  very  interesting  on  their 
own  account,  will  be  discussed  later,  and  will  for  the  present 
onlv  be  used  as  a  means  of  obtaining  values  for  plotting  the 


35 


40  45  50 

P.D.  betiveen  Carbons  in  Volts. 

FIG.  50.— Square  of  Diameter  of  Crater  and  P.D.  between  Carbons  for 

various  Currents  and  Lengths  of  Arc. 
Carbons  :  Positive,  13mm.,  cored  ;  negative,  llmm.,  solid. 

curves  connecting  the  area  of  the  crater  and  the  crater  ratios 
with  the  length  of  the  arc.  Table  XVII.  gives  the  squares  of 
the  diameters  of  the  crater  obtained  from  these  curves,  together 
with  the  square  roots  of  these  squares,  and  the  differences 
between  the  diameters  thus  calculated  and  the  observed 
diameters  given  in  Table  XVI. 


154 


THE  ELECTRIC  ARC. 


Table  XVII. — Squares  of  Diameters  of  Crater  from  Fig.  54, 
Diameters  calculated  from  those  Squares,   and    Differences 
between  those  Diameters  and  Observed  Diameters. 
Carbons :  Positive,  13mm.,  cored ;   negative,  llmm.,  solid. 


*=>  s 

l=i. 

J=2 

Z=3 

l=t 

is, 

n 

!  Differ- 
fj*    1    d     \  ence  of 
\  Diam. 

* 

d 

Differ- 
ence of 
Diam. 

d* 

d 

Differ- 
ence of 
Diam. 

* 

d 

Differ- 
ence of 
Diam. 

4 
7 
10 
15 
iiO 

9-9!  3-14  1  +  0-04 
15-6  3-95|  -0-25 
21-1  14-59  \  +  0-34 
30-3  5-5  1+0-05 
39-5  6-28-0-^ 

11-7 

17-4 
22-9 
32-1 
41-3 

3-42 
4-17 
4-78 
5'67 
6-43 

-0-38 
-0-03 
+  0-03 
+  0-07 
+  0-03 

12-6 
18-3 
23-8 
33-0 
42-2 

3-55 
4-28 
4-88 
5-74 
6-49 

0 
+  0-08 

+  0-39 
+  0-09 

13-2 
18-9 
24-4 
33-6 
42-8 

3-63 
4-35 
4-94 
5-80 
6-54 

+  0-08 
-  0-05 
+  0-04 
0 
-  0-06 

Fourteen  of  the  nineteen  diameters  taken  from  the  curves 
differ  from  the  observed  diameters  by  less  than  O'lmm.  Of 
the  other  five  one  differs  by  0'12mm.,  one  by  0'25mm.  and 
the  other  three  by  between  three  and  four  tenths  of  a  milli- 
metre. Hence  there  are  four  really  bad  points,  two  belonging 
to  the  1mm.  arc,  one  to  the  2mm.  and  one  to  the  3mm.,  and  all 
four  belonging  to  different  currents.  It  seems  pretty  certain 
then,  that  the  curves  in  Fig.  54  do  really  represent  the  relation 
between  the  current  and  the  square  of  the  diameter  of  the 
crater  for  the  different  lengths  of  arc,  and  that  we  may  safely 
use  the  values  obtained  from  them  to  plot  the  curves  con- 
necting the  length  of  the  are  with  the  square  of  the  diameter 
of  the  crater  for  constant  currents.  These  curves  are  given 
in  Fig.  51,  and  verify  the  first  prediction  made  about  the 
area  of  the  crater  in  Chap.  IV.,  namely,  that  it  would 
increase  as  the  length  of  the  arc  increased  with  a  constant 
current. 

In  order  to  calculate  the  crater  ratios  for  each  current  and 
length  of  arc  from  Table  XVII.  it  is  necessary  to  know  the 
diameter  of  the  core  of  the  positive  carbon  employed.  This 
was  3mm.,  and  therefore  to  obtain  the  ratio  of  the  area  of  the 
core  to  the  area  of  the  crater — that  is,  the  soft  crater  ratio — the 
number  9  must  be  divided  by  each  of  the  squares  of  diameter 
given  in  Table  XVII.  The  hard  crater  ratio,  that  is,  the  ratio  of 
the  area  of  hard  carbon  in  the  surface  of  the  crater  to  the  area 
of  the  crater,  is  obtained  by  subtracting  the  soft  crater  ratio  from 
1  in  each  case,  for  if  s  be  the  area  of  soft  carbon  and  h  the  area 


AREA   OF  CEATEE. 


155 


of  hard  carbon  in  the  surface  of  the  crater,  and  if  a  be  the  area 
of  the  crater,  then 


h     a  —  s     +      s 

= =1  -  -. 

a        a  a 


45 


40 


10AMP§5§2. 


30 


Q25 
•& 


20 


15 


10 


0  12345 

Length  of  Arc  in  Millimetres. 

FIG.  51. — Square  of  Diameter  of  Crater  and  Length  of  Arc  for  various 
Constant  Currents. 

Carbons  :  Positive.  13mm.,  cored  ;  negative,  llmm.,  solid. 


156 


THE  ELECTRIC  ARC. 


Table  XVIII.  gives  the  soft  and  hard  crater  ratios  with  the 
corresponding  currents,  P.D.s,  and  lengths  of  arc. 

Table  XVIII.— Crater  Ratios  calculated  from  Table  XVII.,  ivith 

corresponding  Currents,  P.Ds.,  and  Lengths  of  Arc. 
Carbons:  Positive,  13mm.,  cored;   negative,  llmm.,  solid. 


I  to  M  M  1  Current  in 
1  ocno<l^  |  Ampere8. 

Z=l. 

Z=2. 

1  =  3. 

l=i. 

P.D. 
in 

volts. 

Soft 
crater 
ratio. 

Hard 
crater 
ratio. 

P.D. 
in 
volts. 

Soft 
crater 
ratio. 

Hard 

crater 
ratio. 

P.D. 
in 

Volts. 

~56:0 
49-0 
46-8 
45-2 
44-9 

Soft 
crater 
ratio. 

Hard 
crater 
ratio. 

P.D. 
in 

volts. 

Soft 
crater 
ratio. 

Hard 
crater 
ratio. 

38-75 
38-0 
38-6 
39-8 
40-9 

0-909 
0-577 
0-427 
0-297 
0-228 

0-091 
0-423 
0-573 
0-703 
0-772 

51-0 
4515 
43-3 
43-2 
43-3 

0-769 
0517 
0-393 
0-280 
0-218 

0-231 
0-483 
0-607 
0-720 
0-782 

0-714 
0-492 
0-378 
0-273 
0213 

0286 
0-508 
0-622 
0727 
0-787 

58-6 
521 
49-7 
47-75 
46-6 

0-6820-318 
04760-524 
03690631 
0-2680732 
02100-790 

From  this  table  the  curves  in  Fig.  52  have  been  constructed, 
connecting  the  soft  crater  ratio  with  the  length  of  the  arc  for 


01234 

Length  of  Arc  in  Millimetres. 

FIG.  52. — Soft  Crater  Ratio  and  Length  of  Arc  for  various  Constant 

Currents. 
Carbons  :  Positive,  13mm.,  cored;  negative,  llmm.,  solid. 


CRATER  RATIOS. 


157 


the  various  constant  currents.  These  curves  completely  verify 
the  second  and  third  predictions  made  in  Chap.  IV.,  namely,, 
that  the  rate  of  change  of  soft  crater  ratio  with  change  of  length 
would  diminish  as  the  length  of  the  arc  increased,  and  that  the 
change  of  soft  crater  ratio  with  change  of  length  would  be 
smaller,  and  the  rate  of  change  more  nearly  constant,  the  larger 
the  current. 

For,  firstly,  all  the  curves  are  steeper  with  short  arcs  than 
with  long  ones,  so  that  an  increase  of  length  from  1mm.  to  2mm. 
is  marked  by  a  much  greater  change  in  the  soft  crater  ratio 
than  an  increase  from  3mm.  to  4mm.  Secondly,  the  20  ampere 


38        40 


42        44        46        48         50        52        54 
P.D.  between  the  Carbons  in  Volts. 


58       60 


FIG.  53. — Hard  Crater  Ratio  and  P.D.  between  Carbons  for  various 
Constant  Currents. 

Carbons  :  Positive,  13mm.,  cored  ;  negative  llmm.,  solid. 

curve  is  far  less  steep  than  the  4  ampere  curve,  showing  that, 
for  a  given  change  in  the  length  of  the  arc,  the  sofb  crater 
ratio  alters  less  with  a  large  than  with  a  small  current. 
Thirdly,  the  20  ampere  curve  is  much  nearer  to  a  straight  line 
than  the  4  ampere  curve,  showing  that  the  change  of  soft 
crater  ratio  with  change  of  length  is  more  nearly  constant  the 
larger  the  current. 

Hence,  the  theory  of  the  dependence  of  the  P.D.  on  the  sofb 


158  THE  ELECTRIC  AEG. 

crater  ratio,  with  a  cored  positive  carbon,  is  fully  confirmed  by 
these  curves,  obtained  from  observations  on  the  area  of  the  crater. 

The  relation  between  the  hard  crater  ratio  and  the  P.D. 
between  the  carbons  is  shown  in  Fig.  53.  The  connection 
evidently  follows  a  straight  line  law,  and  is  such  that  the  P.D. 
increases  as  the  hard  crater  ratio  increases,  that  is  to  say,  as  the 
proportion  of  hard  carbon  in  the  surface  of  the  crater  increases, 
which  was  to  be  expected  from  what  has  gone  before. 

Many  other  curves  might  be  drawn  by  using  the  numbers  in 
Table  XVIII.  in  various  ways,  but  as  those  already  drawn 
fully  confirm  the  theory  given  in  Chap.  IV.,  concerning  the 
interdependence  of  the  crater  ratios  and  the  P.D.  between  the 
carbons,  the  remainder,  with  the  deductions  to  be  made  from 
them,  may  be  left  to  the  ingenuity  of  the  reader. 

Before  leaving  the  subject  of  the  area  of  the  crater  the 
curves  in  Fig.  54,  showing  the  connection  between  the  area  of 
the  crater  and  the  current  flowing  when  the  length  of  the  arc 
is  constant,  must  be  examined.  A  straight  line  law  connects 
these  two  variables,  but  the  area  of  the  crater  is  not,  as 
Andrews  concluded  (see  p.  39),  from  his  measurements  of  the 
crater,  proportional  to  the  current.  It  is  the  area  of  the 
crater  minus  a  constant  depending  on  the  length  of  the  arc 
that  varies  as  the  current,  at  any  rate  when  a  cored  positive 
carbon  is  used.  From  the  figure  it  appears  very  likely  that 
Andrews'  conclusion  may  be  true  when  the  length  of  the  arc 
is  0,  for  the  distance  between  the  lines  for  length  of  arc  1  and 
length  of  arc  0  would  be  just  about  right  if  the  latter  passed 
through  the  origin. 

The  fact  that  the  lines  connecting  the  area  of  the  crater  with 
the  current  for  the  various  constant  lengths  of  arc  are  all 
parallel  to  one  another  leads  to  two  very  interesting  conclusions. 
The  first,  that  the  change  of  crater  area  accompanying  a  change 
of  current  is  independent  of  the  length  of  the  arc,  and  the 
second,  that  the  change  of  crater  area  accompanying  a  change 
in  the  length  of  the  arc  is  independent  of  the  current.  For 
example,  an  increase  of  current  from  4  to  10  amperes  is  accom- 
panied by  an  increase  of  11'2  square  millimetres  in  the  square 
of  the  diameter  of  the  crater,  whether  the  arc  be  1mm.,  2mm., 
3mm.  or  4mm.  in  length ;  similarly  an  increase  in  the  ength 
from  1mm.  to  4mm.  is  accompanied  by  an  increase  of  3*3 


DEPTH  OF  CRATER. 


159 


square  millimetres  in  the  square  of  the  diameter  of  the  crater, 
whatever  the  current  may  be,  from  4  to  20  amperes.  Thus, 
although  the  area  of  the  crater  increases,  both  with  an  increase 
of  the  current  and  an  increase  of  the  length  of  the  arc,  the 
change  of  area  with  change  of  current  is  independent  of  the  length 
of  the  arc,  and  the  change  of  area  with  change  of  length  is  inde- 
pendent of  the  current  flowing. 


45 


40 


~  35 


v  30 


.S  25 


S  15 


14 


16 


0  2  4  6  8  10  12 

Current  in  Amperes. 

FIG.  54.  —  Square  of  Diameter  of  Crater  and  Current  for  various  Constant 
Lengths  of  Arc. 

Carbons  :  Positive,  13mm.,  cored  ;  negative,  llmm.,  solid. 

It  has  been  observed  (p.  144)  that  the  depth  of  the  crater  had 
very  little,  if  any,  influence  on  the  P.D.  between  the  carbons. 
In  order  to  see  whether  this  hollowing  out  of  the  crater  (which 
is  very  great  in  cored  carbons)  really  had  any  influence  on  the 
P.D.,  measurements  were  taken  of  the  depths  of  craters  with 
different  currents  and  lengths  of  arc.  The  results  are  given  in 
Table  XIX.  The  carbons  used  were  the  same  as  those  used 


160 


THE  ELECTEIC  ARC. 


for  measuring  the  diameter  of  the  crater,  13mm.  cored  positive, 
and  llmm.  solid  negative,  in  fact  the  measurements  of 
diameter  and  depth  were  made  on  the  same  craters.  The 
measurements  were  made  by  means  of  a  microscope  with  a 
micrometer  screw  arrangement  for  focussing.  The  edge  of 
the  crater  was  first  brought  into  focus  and  the  reading  taken 
on  the  micrometer,  then  the  bottom  of  the  crater  was 
brought  into  focus,  and  the  reading  again  taken.  The 
difference  of  the  two  readings  gave  the  depth  of  crater.  Great 
care  was  taken  that  the  craters  should  be  completely  formed 
with  the  given  current  and  length  of  arc,  before  the  depth 
was  taken. 

Table   XIX. — Depth   of  Crater   with   Different    Currents   and 

Lengths  of  Arc. 
Carbons:  Positive,  ISmm.,  cored ;    negative,  llmm. y  solid. 


Length  of 

Current 

Depth  of 

Length  of 

Current 

Depth  of 

arc  111 

in 

crater  in 

arc  in 

in 

crater  in 

millimetres 

amperes. 

millimetres. 

millimetres 

amperes. 

millimetres. 

1 

6 

0-96 

3 

20 

1-C6 

] 

10 

1-33 

3 

30 

0-98 

1 

15 

1-6 

6 

6 

0-72 

1 

20 

1-38 

6 

10 

0-55 

1 

28 

1-266 

6 

15 

0-63 

3 

6 

0'82 

6 

20 

0-77 

3 

10 

0-95 

6 

25 

0-65 

3 

15 

0-96 

6 

30 

0-65 

It  is  not,  of  course,  pretended  that  these  measurements  of 
the  depth  of  the  crater  were  absolutely  accurate,  a  small  ex- 
crescence upon  the  edge  of  the  crater  or  a  slight  irregularity 
of  form,  such  as  those  who  are  familiar  with  arcs  will  recog- 
nise as  being  of  constant  occurrence,  would  tend  to  obscure 
the  real  depth  of  crater ;  but  the  general  character  of  the  change 
in  the  depth,  with  variation  of  current  and  length  of  arc,  is 
very  apparent. 

It  is  evident  that  with  a  given  current  the  depth  of  the 
crater  is  greater  the  shorter  the  arc,  and  therefore  the 
percentage  increase  of  length  of  arc  caused  by  the  depth  of 
the  crater  increases  rapidly  as  the  arc  is  shortened.  For  example, 
with  a  current  of  6  amperes  the  depth  of  the  crater  increases 


DEPTH  OF  CRATER.  161 

the  apparent  length  of  the  6mm.  arc  by  12  per  cent.,  the 
apparent  length  of  the  3mm.  arc  by  27  per  cent,  and  the 
apparent  length  of  the  1mm.  arc  by  96  per  cent. 

With  a  given  length  of  arc  the  depth  of  the  crater  appears 
to  increase  as  the  current  increases,  to  reach  a  maximum  with 
currents  of  from  15  to  20  amperes  and  then  to  diminish. 

Whether  the  depth  of  the  crater  per  se  has  any  influence 
either  in  raising  or  lowering  the  P.D.  it  would  require  much 
more  detailed  experiments  to  determine,  but  at  any  rate  the 
effect  is  so  completely  masked  by  the  far  greater  influence  of 
the  area  of  the  crater  (which  has  been  shown  to  be  sufficient 
alone  to  account  for  the  differences  between  the  curves  for 
cored  and  solid  carbons)  that  it  may  be  altogether  neglected. 
For  example,  there  is  nothing  in  the  curves  for  constant  length 
of  arc  (Fig.  40)  to  connect  the  P.D.  between  the  carbons  with 
the  depth  of  the  crater,  for  there  Id  no  maximum  P.D.  with  a 
current  of  15  amperes  for  the  Irnm.  arc  as  there  is  a  maximum 
depth  of  crater,  nor  is  there  any  maximum  P.D.  with  any 
particular  current  for  the  other  lengths  of  arc.  We  may 
therefore  conclude  that  there  is  no  evidence  to  prove  that  the 
depth  of  the  crater  has  any  influence  on  the  P.D.  between  the 
carbons. 

A  glance  at  Figs.  39,  40  and  41  (pp.  128-130)  is  sufficient 
to  show  the  general  character  of  the  changes  in  the  curves 
caused  by  varying  the  diameters  of  the  carbons  employed. 
The  chief  of  these  is  the  change  in  the  largest  silent  current, 
which  will  be  dealt  with  in  the  chapter  on  hissing  arcs. 

As  regards  those  portions  of  the  curves  which  refer  to  silent 
arcs,  it  will  be  seen  that  the  P.D.  required  to  send  a  particular 
current  through  a  given  length  of  arc  depends  comparatively 
little  on  the  cross-section  of  the  carbons,  for  although  the  carbons 
for  the  curves  in  Fig.  39  had  about  four  times  the  cross-section 
of  the  carbons  for  the  curves  in  Fig.  41,  yet  the  P.D.  for  any 
given  current  and  length  of  arc  does  not  in  any  case  differ 
with  the  two  sets  of  carbons,  by  as  much  as  14  per  cent.,  and 
in  most  cases  it  differs  by  far  less  than  that. 

In  Table  XX.  some  examples  are  given  illustrating  this  point. 

Some  of  the  P.Ds.  for  a  given  length  of  arc  and  current  in 
this  table  are  almost  identical  for  the  three  different  pairs  of 
carbons ;  for  example,  43,  43  and  43'7  volts  for  a  2mm.  aro 

M 


162 


THE  ELECTHIG  AEC. 


with  10  amperes,  or,  again,  44'5,  45  and  45 -8  for  a  3mm.  arc 
with  15  amperes.  In  many  other  cases,  however,  there  is  a 
marked  difference  in  the  P.Ds.  ;  for  example,  36,  37 '5  and 
41 '5  volts  for  a  1mm.  arc  with  6  amperes.  We  must  therefore 
conclude  that  the  steady  value  of  the  P.D.  between  the  carbons 
while  depending  principally  on  the  particular  current  and 
length  of  arc,  does  also  depend  on  the  diameters  of  the  carbons, 

Table  XX. — Influence  of  Diameters  of  Carbons  on  P.D.  between 

them. 


Length 

Current 

P.D.  between  carbons  for 

of  arc  in 
millimetres. 

in 

amperes. 

+  18mm.  cored 
-  15mm.  solid. 

+  13mm.  cored. 
—  llmm.  solid. 

+  9mm.  cored. 
-  8mm.  solid. 

0-5 

6 

33-0 

36-7 

1-0 

6 

36-0 

37-5 

41-5 

2-0 

6 

47-0 

46-0 

44-2 

3-0 

6 

50-5 

50-2 

48-4 

4-0 

6 

53-0 

54-0 

53-8 

5-0 

6 

54-75 

56-0 

55-8 

0-5 

10 

34-9 

39-0 

1-0 

10 

36-0 

38-5 

42-0 

2-0 

10 

43-0 

43-0 

43-7 

3-0 

10 

46-5 

46-7 

46-2 

4-0 

10 

47-5 

49-7 

50-0 

5-0 

10 

49-75 

52-0 

51-8 

0-5 

15 

36-5 

hissing. 

1-0 

15 

37-5 

39-7 

43-0 

2-0 

15 

42-0 

43-0 

44-0 

3-0 

15 

44-5 

45-0 

45-8 

4-0 

15 

45-8                   47-5 

48-5 

5-0 

15 

48-0 

50-5 

50-2 

This  is  seen  still  more  plainly  from  the  curves  in  Fig.  55, 
which  connect  P.D.  with  length  of  arc,  for  constant  currents 
of  6  and  15  amperes,  with  each  of  the  three  pairs  of  carbons. 

These  curves  show  that  while,  with  a  current  of  6  amperes, 
the  P.D.  is  sometimes  the  same  for  all  three  carbons,  sometimes 
highest  with  the  largest  carbons,  and  sometimes  with  the 
smallest;  with  the  larger  current  of  15  amperes  the  P.D.  is 
uniformly  highest  with  the  smallest  carbons  and  lowest  with 
the  largest. 

Such  variations  in  the  P.D.  for  the  same  current  and  length 
of  arc  with  different  sized  carbons  have  probably  two  causes, 


fiC 


55 


£   50 


163 


<=}  40 

0, 


35 

30 

55 

50 
1 

s   45 

o 

r 

35 
30 


0123 

Length  of  Arc  in  Millimetres. 


A.    6  Amperes. 


012345 
Length  of  Arc  in  Millimetres. 

B.  15  Amperes. 
55. — P.D.  and  Length  of  Arc  for  Constant  Currente  of  (A)  6  Amperes, 

and  (B)  15  Amperes. 

Carbons  :  Positive,  18mm.,  cored  ;   negative,  15mm.,  solid. 
,,         13mm.       „  ,,        llmm.       „ 

„          9mm.      „  „         8mm.      „ 

MM2 


164 


THE  ELECTRIC  ARC. 


which  may  sometimes  aid  and  sometimes  counteract  one 
another  : — (1)  The  different  degrees  of  cooling  to  which  the 
crater  is  subjected  by  the  difference  of  mass  of  the  cold  carbon 
round  it ;  (2)  The  difference  in  the  crater  ratios  caused  by  the 
core  having  a  different  diameter  in  each  of  the  three  carbons ; 
for  the  core  of  the  18mm.  carbon  was  4mm.,  that  of  the  13mm. 
was  3mm.,  and  that  of  the  9mm.  was  2mm.  in  diameter.  Hence, 
with  the  same  area  of  crater,  the  hard  crater  ratio,  to  which  the 
P.D.  has  been  shown  to  have  some  sort  of  proportionality, 
would  be  greatest  in  the  smallest  carbon,  and  least  in  the 
greatest.  If,  therefore,  the  area  of  the  crater  were  independent 
of  the  size  of  the  positive  carbon,  we  should  expect  the  P.D. 
for  a  given  current  and  length  of  arc  to  be  greatest  with  the 
smallest  carbon  and  least  with  the  greatest,  as,  indeed,  it  is 
with  a  current  of  15  amperes. 


10 


01234567 
Length  oj  Arc  in  Millimetres, 

FIG.  56. — Apparent  Resistance  and  Length  of  Arc  for  various  Constant 
Currents, 

Carbons :  Positive,  18mm.,  cored  ;  negative,  13mm.,  solid. 

The  curves  connecting  apparent  resistance  with  length  of 
arc  (Figs.  56,  57  and  58)  have  next  to  be  considered, 
The  ordinates  of  these  curves  were  obtained  by  dividing  the 
P.D.  for  each  length  of  arc  by  each  current  used,  after  the 
current  had  in  each  case  been  kept  constant  for  a  sufficient 


APPARENT  RESISTANCE. 


165 


length  of  time  for  the  carbons  to  be  properly  shaped  for 
the  particular  current  and  length  of  arc.  The  abscissae 
are  the  corresponding  lengths  of  arc,  the  current  being  the 
same  for  all  the  points  on  any  one  curve. 

These  curves  are   naturally  of  the   same  form  as  those  in 
Figs.  45,  46  and  47,  for  the  abscissae  are  the  same  in  both  cases, 


16 


-S  12 
o 


42    8 
"8 


20Ar 


25  Amperes. 


012346678 

Length  of  Arc  in  Millimetres. 

FIG.  57. — Apparent  Resistance  and  Length  of  Arc  for  various  Constant 
Currents. 

Carbons  :  Positive,  13mm.,  cored  ;  negative,  llmm.,  solid. 

and  the  ordinates  of  the  curves  in  Figs.  56,  57  and  58  may  be 
obtained  from  those  in  Figs.  45,  46  and  47  by  dividing  those 
belonging  to  each  curve  by  the  corresponding  constant 
current. 


1C6 


THE  ELECTRIC  AUG. 


The  meaning  of  the  peculiar  shapes  taken  by  these  curves 
has  already  been  fully  discussed  (pp.  139-147),  and  need  not 
therefore,  be  further  enlarged  upon,  for  everything  that  has 
been  said  concerning  the  curves  connecting  the  P.D.  between 
the  carbons  with  the  length  of  the  arc  for  constant  currents 
with  a  cored  positive  carbon,  applies  equally  to  the  apparent 
resistance  curves  in  Figs.  56,  57  and  58. 

In  1886  Messrs.  Cross  and  Shepard  constructed  resistance 
curves  of  this  kind  for  solid  carbons,"*  and  found  that  in 
every  case  they  obtained  straight  lines  for  both  silent  and 
hissing  arcs,  showing  that  the  apparent  resistance  of  the  arc 


10 


2  3  4  5  6.7 

Length  of  Arc  in  Millimetres. 

FIG.  58. — Apparent  Resistance  and  Length  of  Arc  for  various  Constant 
Currents. 

Carbons  :  Positive,  9nim.,  cored  ;  negative,  8mm.,  solid. 

minus  a  constant  varied  directly  as  the  length  of  arc.     Thus 
they  showed  that  Edlund's  formula 
r  =  a  +  b  I, 

where  r  is  the  apparent  resistance  of  the  arc,  I  the  length  of 
arc,  and  a  and  b  are  constants  which  depend  on  the  currents 
and  the  carbons,  is  applicable  to  the  hissing  as  well  as  to  the 
silent  arc. 

*  Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  June  16, 1886. 


CONSTANT  P.D.  167 

Ths  results  of  my  own  experiments  with  solid  carbons  agree 
with  this  equation  ;  as  a  reference  to  Fig.  44  will  show  for 
silent  arcs,  and,  as  will  be  seen  in  Chap.  X.,  for  hissing  arcs.  It 
has  already  been  mentioned  that  the  ordinates  of  each  curve  in 
Fig.  44  have  only  to  be  divided  by  the  number  representing 
the  constant  current  corresponding  with  that  curve  to  give  the 
apparent  resistance  of  the  arc  in  each  case,  therefore  it  has  not 
been  thought  necessary  to  plot  separate  resistance  curves  for 
solid  carbons. 

The  sets  of  curves  in  Figs.  45,  46  and  47  were  drawn  by  taking 
a  number  of  vertical  sections  of  the  curves  in  Figs.  39,  40  and  41 
(pp.  128-130).  In  a  similar  way  a  set  of  curves  can  be  drawn 
for  each  of  the  three  pairs  of  carbons  by  taking  a  number  of 
horizontal  sections  of  the  curves  in  those  figures,  and  the 
results  so  obtained  show  the  connection  between  current  and 
length  of  arc  for  various  constant  P.Ds. 

Dealing  with  Fig.  40  in  this  way,  we  obtain  Fig.  59  for  the 
13mm.  cored  positive  carbon  and  the  11  mm.  solid  negative 
carbon ;  but  it  is  to  be  remembered  that  the  points  on  these 
curves  were  not  obtained  by  keeping  the  P.D.  constant  until 
the  current  became  constant  for  each  length  of  arc,  but  by 
keeping  the  current  constant  until  the  P.D.  became  constant 
for  each  length  of  arc.  In  fact,  current  and  length  of  arc 
were  kept  constant,  and  not  P.D.  and  length  of  arc.  From 
the  curves  in  this  figure  we  can  see  the  current  that  each 
particular  P.D.  will  finally  send  through  each  length  of  silent 
arc  with  this  pair  of  carbons,  as  well  as  the  maximum  length 
of  silent  arc  that  can  be  maintained  with  any  given  P.D. 
between  the  carbons. 

To  obtain  this  maximum  length  for  any  constant  P.D. 
we  have  merely  to  draw  a  vertical  tangent  to  the  correspond- 
ing curve,  and  observe  where  it  cuts  the  axis  of  length  of  arc. 
For  example,  the  vertical  tangent  to  the  curve  corres- 
ponding with  a  constant  P.D.  of  43'5  volts  between  the 
carbons,  cuts  the  axis  of  length  at  about  2i4mm.  Hence, 
while  a  P.D.  of  43 '5  volts  can  produce  a  silent  arc  of 
any  length  between  1  and  about  2 '4mm.:,  it  can  produce 
TIO  permanent  silent  arc  longer  than  2*4 mm.  with  these  carbons. 

If,  starting  with  a  small  current,  the  P.D.  between  the 
carbons  be  kept  constant  and  the  arc  gradually  lengthened, 


168  THE  ELECTRIC  ARC. 

the  current  will  gradually  increase  until  a  certain  value  is 
irrived  at,  when  either  the  current  begins  to  decrease  or  the 
ire  becomes  unstable;  for  example,  with  the  constant  P.D, 
of  48 '5  ^olts  this  happens  with  a.  current  of  about  32  amperes 
if  the  current  has  been  kept  at  a  fixed  value  for  some  time 
for  each  length  of  arc. 

When  the  constant  P.D.  is  less  than  about  46  volts  the 
curves  in  Fig.  59  bend  bask  before  the  condition  of  instability 
is  reached,  so  that  for  some  lengths  of  silent  arc  there 
are  two  very  different  currents  permanently  produced  with 
the  same  P.D.  For  example,  with  the  constant  P,D.  of 
45  volts  a  current  of  about  either  15  or  of  30  amperes  may 
pass  and  maintain  a  silent  arc  of  3mm.  With  a  constant 
P.D.  of  43-5  volts  a  silent  arc  of  2mm.  can  be  produced  with 
a  current  of  about  8f8  or  28  amperes,  and  a  constant  P.D. 
of  41*5  volts  will  send  a  current  of  about  2*8  or  of  23  amperes 
silently  through  an  arc  of  1mm. 

For  a  constant  P.D.  of  48 '5  volts,  on  the  contrary,  there 
is  only  one  current  that  will  pass  silently  for  each  length  of  arc 
and  remain  constant,  this  current  being  about  4*5  amperes 
when  the  arc  is  2mm.  long,  about  7'5  amperes  when  it  is  3mm., 
about  12  amperes  for  a  4mm.  arc,  and  about  32  amperes  when 
the  arc  is  lengthened  to  5mm. 

The  arc  now  becomes  unstable,  and  the  curve  shifts  sideways, 
and  continues  as  a  vertical  straight  line  for  a  much  longer 
hissing  arc. 

From  the  curves  in  Fig.  59  it  follows  that  when  the 
P.D.  is  kept  constant  at,  say,  46 '5  volts  and  the  arc  is 
lengthened  from  1mm.  to  5mm.  the  current  increases  in  value ; 
whereas  when  it  is  kept  at  about  44  volts  a  wide  range  of  cur- 
rent can  be  obtained  with  the  same  length  of  arc,  and,  lastly, 
that  when  the  constant  value  of  the  P.D.  is,  say,  41-5  volts, 
lengthening  the  arc  sometimes  diminishes  the  current. 

These  facta  have  been  already  stated  and  explained  in  con- 
nection with  the  curves  in  Fig.  40  (p.  129)  from  which  the  curves 
in  Fig.  59  have  been  deduced.  But  at  the  time  the  experiments 
were  made  it  appeared  to  be  so  astonishing,  as  well  as  novel, 
that  a  change  in  the  steady  value  of  the  P.D.  from,  say,  46 
to  41  volts  should  entirely  alter  the  way  in  which  the  current 
varied  wiu,h  length  of  arc,  increasing  in  the  former  case  with  the 


CONSTANT  P.D. 


169 


1234  567 

Length  of  Arc  in  Millimetres. 

FIG.  59. — Current  and  Length  of  Arc  for  various  Constant  P.Ds. 
Carbons  :  Positive,  13mm.,  cored ;  negative,  llmm.,  solid. 


170  THE  ELECTRIC  ARC. 

lengthening  of  the  arc,  and  decreasing  in  the  latter,  that  it  seemed 
worth  while  to  test  these  facts  by  actually  experimenting  on 
arcs  with  various  constant  P.Ds. 

The  experiments  were  tried  in  two  ways — (i)  the  P.D.  waa 
kept  constant  by  using  accumulators  with  no  external  resistance 
beyond  that  of  the  arc ;  (2)  a  dynamo  was  used,  and  the  P.D. 
between  the  ends  of  the  carbons  was  kept  constant  by  means  of 
a  wide  range  of  external  resistance. 

With  the  dynamo,  a  constant  P.D.  of  55  volts  was  main- 
tained between  the  ends  of  the  carbons  in  the  following 
way :  The  arc  was  struck  with  a  large  amount  of  resistance 
in  circuit,  the  carbons  were  then  separated  to  the  desired  extent, 
the  resistance  being  altered  meantime  until  a  P.D.  of  55  volts 
was  obtained ;  then  the  arc  was  kept  at  the  given  length  for 
some  time,  and  the  P.D.  kept  at  55  volts  by  means  of  the 
external  resistance,  until  the  current  appeared  to  have  reached 
its  steady  value,  when  the  reading  was  taken.  The  carbons 
used  were  13mm.  cored  positive  and  llmm.  solid  negative. 

It  was  found  that  with  a  P.D.  of  55  volts  a  current  of  27 
amperes  could  be  maintained  steadily  flowing  through  an  arc 
of  2mm. ;  a  current  of  3-3  amperes  would  flow  steadily 
through  an  arc  of  3mm.,  and  that  the  current  that  could  be 
maintained  permanently  flowing  through  the  arc  increased 
steadily  as  the  length  of  the  arc  was  increased,  thus  proving 
that  the  curves  for  constant  P.D.  of  46*5  volts  and  upwards  in 
Fig.  59  were  correct  in  character  when  a  cored  positive  carbon 
was  used. 

The  second  problem,  Does  the  current  sometimes  decrease  as 
the  length  of  arc  is  increased  with  short  arcs  and  large  steady 
currents  ?  was  tried  with  the  dynamos  and  external  resistance 
in  the  same  way  as  before,  and  an  answer  was  obtained  in  the 
affirmative.  It  was  found  that  with  a  constant  P.D.  of  4 2 '5 
volts  a  current  of  22  amperes  could  be  maintained  steadily 
flowing  through  an  arc  of  l'3mm.,  while  a  current  of  19 '5 
amperes  only  would  flow  permanently  through  an  arc  of 
l'5mm.  Thus  it  was  shown  experimentally  that  when  a  cored 
positive  carbon  is  used  with  certain  constant  P.Ds.  the  current 
increased  as  the  arc  was  lengthened,  and  that  with  other  constant 
P.Ds.  the  current  increased  as  the  arc  was  shortened^  was  evident 
therefore  that  there  must  be  an  intermediate  constant  P.D 


CONSTANT  P.D. 


171 


which  would  permanently  maintain  many  different  currents 
with  the  same  length  of  arc  ;  therefore,  all  the  three  cases  sug- 
gested by  the  curves  in  Fig.  59  were  shown  to  be  correct. 

These  experiments,  in  which  the  P.D.  and  length  of  arc  are 
kept  constant  and  the  current  allowed  to  vary,  are  very  difficult 
to  carry  out,  because  each  P.D.  will  only  send  a  current  per- 
manently through  certain  lengths  of  arc,  and  if  you  happen  to 
hit  upon  a  length  of  arc  to  which  the  P.D.  you  are  trying  does 
not  belong,  you  may  have  all  your  pains  for  nothing.  It  may 
take  an  hour  to  find  out  that,  although  you  are  sending  a 
current  through  the  given  length  of  arc  with  the  fixed  P.D. 


40 


50 


60 


30 
Time  in  Minutes. 

FIG.  60.—  Time  record  of  Current  with  Constant  P.D.  of  42'5  volts,  and 

Constant  Length  of  Arc  of  1mm. 
Carbons:  Positive,  13mm.,  cored  ;  negative,  llmm.,  solid. 

all  the  time,  yet  that  current  will  not  remain  constant,  but  will 
change  continually.  If  the  current  is  increasing,  it  rushes  up 
rapidly,  and  then  if  the  P.D.  is  maintained  constant  by  means 
of  accumulators  with  no  interposed  resistance  the  cut-out  goes. 
Or  if,  to  prevent  this  occurring,  you  endeavour  to  maintain 
the  P.D.  between  the  carbons  constant  by  means  of  a  dynamo 
with  interposed  resistance,  the  arc  suddenly  hisses  and  the 


172  THE  ELECTRIC  ARC. 

P.D.  falls  in  spite  of  all  attempts  to  prevent  it  by  rapidly  ad- 
justing the  interposed  resistance.  If,  on  the  other  hand,  the 
current  is  decreasing,  the  arc  flickers  and  goes  out. 

Fig.  60  shows  very  well  what  happens  when  the  P.D.  and 
length  of  arc  are  kept  constant  and  the  current  is  allowed  to 
vary.  The  current  started  at  20'6  amperes  and  gradually 
diminished  till  it  reached  its  steady  value  of  about  1*6  amperes 
nearly  50  minutes  after  starting.  The  larger  steady  current 
of  about  28  amperes  that  might  have  been  maintained  with  the 
same  P.D.  and  length  of  arc  according  to  Fig.  40  was  too  near 
the  hissing  point  to  be  attempted  by  this  method.  The 
meaning  of  the  difficulty  experienced  in  maintaining  the  arc 
with  a  constant  P.D.  and  a  small  external  resistance  will  be 
explained  when  the  mathematical  relations  of  the  variables  of 
the  arc  are  considered  in  Chap.  VIII. 


SUMMARY. 

THE  AREA  OF  THE  CRATER  AND  CRATER  RATIOS 

Silent  Arcs. 
With   Constant   Currents. 

I.  A  straight  line  law  connects  the  area  of  the  crater  with 
the  P.D.  between  the  carbons. 

II.  The  area  of  the  crater  increases  as  the  length  of  the  arc 
is  increased. 

III.  The  rate  of  change  of  soft  crater  ratio  with  change  of 
length  diminishes  as  the  length  of  the  arc  increases. 

IV.  The  change  of  soft  crater  ratio  with  change  of  length  is 
smaller  and  the  rate  of  change  more  nearly  constant  the  larger 
the  current. 

V.  The  soft  crater  ratio  diminishes  and  the  hard  crater  ratio 
increases  as  the  length  of  the  arc  increases. 

VI.  The  change  in  the  area  of  the  crater  with  change  of 
length  is  independent  of  the  current  flowing. 

With  Constant  Lengths  of  Arc. 

VII.  The  area  of  the  crater  increases  as  the  current  increases. 

VIII.  The  change  in  the  area  of  the  crater  with  change  of 
current  is  independent  of  the  length  of  the  arc. 


SUMMARY.  173 

THE  DEPTH  OF  THE  CRATER. 

IX.  There  is  no  evidence  to  prove  that  the  depth  of  the 
crater  has  any  influence  on  the  P.D.  between  the  carbons, 

INFLUENCE  OF  THE  DIAMETERS  OF  THE  CARBONS  ON  THE  P.D. 

BETWEEN    THEM    WITH    CORED    POSITIVE    CARBONS. 

X.  With   cored   carbons   the    P.D.    accompanying   a  given 
current  and  length  of  arc  is  in  some  measure  influenced  by  the 
diameters  of  the  carbons,  partly  because  of  the  greater  or  less 
mass  of  carbon  to  be  warmed  up,  partly  because  the  diameter 
of  the  core  is  different  with  different  sized  carbons. 

CURVES  CONNECTING   APPARENT   RESISTANCE   AND  LENGTH   OF 
ARC  WITH  CONSTANT  CURRENTS. 

XI.  The  curves  connecting  the  apparent  resistance  of  the 
arc  with  its  length  for  constant  currents  are  straight  lines  with 
solid  carbons,  but  bend  down  towards  the  axis  of  length  for 
short  arcs  and  small  currents  when  a  cored  positive  carbon  is 
used. 

CURVES  CONNECTING  CURRENT  AND  LENGTH  OP  ARC  FOR 
CONSTANT  P.D. 

XII.  When   the   P.D.  is   constant,   with   a   cored   positive 
carbon,  lengthening  the  arc  may  increase  the  current,  or  leave 
it  unchanged,  or  diminish  it.     This  depends  on  the  original 
current  and  length  of  arc,  and  on  the  cross-section  of  the  core. 


CHAPTER  VI. 


CURVES  CONNECTING  POWER  WITH  LENGTH  OF  ARC  FOR  CONSTANT 
CURRENTS,  AND  POWER  WITH  CURRENT  FOR  CONSTANT  LENGTHS 
OF  ARC.  EQUATION  CONNECTING  P.D.,  CURRENT,  AND  LENGTH 
OF  ARC  WITH  SOLID  CARBONS.  ANALYSIS  OF  RESULTS  OBTAINED 
BY  EARLIER  EXPERIMENTERS. 

Having  found  it  a  very  tedious  and  lengthy  process  to 
obtain  a  steady  P.D.  with  small  currents,  I  started  my  experi« 
ments  for  finding  the  true  connection  between  the  P.D.,  the 
length  of  the  arc,  and  the  current,  when  the  arc  was  in  a  stable 
condition,  by  using  only  currents  of  5  amperes  and  upwards 
and  I  found  the  steady  P.D,  that  would  send  each  current 
through  lengths  of  arc  varying  from  1mm.  to  7mm.  The 
currents  used  were  5,  8,  10,  and  14  amperes  respectively,  the 
largest  current  that  did  not  cause  hissing  for  each  length  of 
arc,  and  two  or  three  of  the  currents  that  did  cause  hissing  •  I 
then  proceeded  to  draw  curves  connecting  P.D.  and  current 
for  the  various  constant  lengths  of  arc,  similar  to  those  in  Figs. 
39,  40  and  41. 

On  attempting,  with  the  data  thus  obtained,  to  find  an 
equation  that  would  fit  all  the  curves,  to  my  dismay  I  dis- 
covered that  there  were  two  equations,  either  of  which  might 
be  correct,  since  all  the  curves  could  be  deduced  with  a  very 
fair  amount  of  accuracy  from  each  of  them.  One  of  these  was 
the  equation  to  a  series  of  ellipses,  the  other  the  equation  to  a 
series  of  hyperbolas.  If  the  curves  were  really  ellipses,  no 
current  of  less  than  about  4  amperes  ought  to  be  able  to 
maintain  an  arc  continuously  with  the  carbons  used ;  whereas 
if  they  were  hyperbolas,  any  current,  however  small,  ought  to 
maintain  an  arc,  provided  a  large  enough  P.D.  could  be 
supplied. 


176  THE  ELECTRIC  ARC. 

Now  the  difficulty,  already  alluded  to,  that  had  always  been 
found  in  maintaining  small  currents,  made  it  appear  as  if  the 
ellipse  equation  were  the  correct  one ;  for  it  seemed  possible 
that,  although  these  currents  could  be  maintained  for  a  short 
time  after  striking  the  arc,  or  changing  the  current  from  a 
larger  to  a  smaller  one,  yet  that,  when  the  excess  of  loose 
carbon  supplied  in  the  previous  state  was  exhausted,  the 
remaining  supply,  kept  up  by  the  small  steady  current,  would 
be  insufficient  to  maintain  the  arc,  and  so  it  would  go  out.  As 
a  matter  of  fact,  it  had  been  found  in  former  experiments  that 
the  arc  did  go  out  again  and  again  after  small  currents  had 
been  flowing  for  a  short  time. 

It  became  necessary,  therefore,  to  decide  whether  the 
conditions  of  the  E,M.F.  of  the  dynamo  and  the  resistance  of 
the  circuit  were  such  as  to  cause  this  instability,  or  whether  it 
really  was  impossible,  with  the  size  of  carbons  I  was  using,  to 
maintain  an  arc,  with  less  than  about  4  amperes,  for  a  sufficient 
length  of  time  for  the  P.D.  to  reach  its  steady  value. 

Using  a  dynamo  producing  a  P.D.  of  about  150  volts 
between  its  terminals,  and  a  large  resistance  in  circuit,  I 
found  that  currents  of  2  amperes  could  be  kept  flowing  long 
enough  for  the  P.D.  to  become  perfectly  steady,  although,  with 
such  small  currents,  the  carbons  took  between  one  and  two 
hours  to  form,  and  therefore  the  P.D.  took  the  same  length  of 
time  to  become  steady. 

Thus  it  was  evident  that  the  curves  were  not  ellipses,  It 
remained  to  prove  whether  they  were  really  hyperbolas,  or  only 
fairly  close  approximations  to  hyperbolas  ;  whether,  in  fact, 
there  was  not  some  extra  term  in  the  true  equation  which 
remained  too  small  to  be  noticed  with  currents  of  5  amperes 
and  upwards,  but  which  would  be  large  enough,  with  smaller 
currents,  to  show  some  discrepancy  between  the  curves  and 
the  equation  I  had  obtained.  It  seemed  advisable,  also,  to 
determine  experimentally  a  great  many  more  points  on  the 
curves  than  I  had  hitherto  done.  I  therefore  decided  to 
make  an  entirely  new  set  of  experiments,  using  the  same 
lengths  of  arc  as  before,  but  taking  many  more  currents,  and 
beginning  with  2  amperes,  so  that  the  points  on  the  curves 
should  be  so  numerous  as  to  preclude  the  possibility  of  any 
mistake  being  made  as  to  their  true  shape. 


P.D.  AND  CUEEENT  CUEVES. 


177 


I 


i 


178  THE  ELECTRIC  ARC. 

Finding  that  even  a  slight  difference  in  the  hardness  of 
the  carbons  caused  a  corresponding  small  change  in  the  steady 
P.D.  necessary  to  send  a  given  current  through  an  arc  of  given 
length,  I  generally  took  two  or  three  readings  of  the  P.D.  for 
each  current  and  length  of  arc,  with  different  carbons,  at 
different  times,  and  used  the  means  of  these  readings  in 
plotting  the  curves.  The  current  was  kept  flowing  at  a 
perfectly  constant  value  through  the  given  length  of  arc  for 
periods  varying  from  a  quarter  of  an  hour  for  large  currents 
to  nearly  two  hours  for  very  small  currents,  before  each  reading 
was  taken,  so  that  there  might  be  no  doubt  as  to  the  P.D. 
having  reached  its  final  steady  value  for  each  current  and 
length  of  arc,  when  the  reading  was  taken.  In  this  way  the 
137  points  were  obtained,  through  which  the  curves  in  Fig.  61, 
(which  is  a  reproduction  of  Fig.  38),  were  plotted. 

There  are  various  ways  of  finding  the  equation  to  the  family 
of  curves  in  Fig.  61.     For  example,  if 
V=/(A,0 

be  this  equation,  where  V  is  the  P.D.  between  the  carbons, 
A  the  current,  and  I  the  length  of  the  silent  arc  as  measured 
on  the  projected  image,  we  may  (1)  begin  by  finding  the 
connection  between  V  and  I  when  A  is  constant,  then  the 
connection  between  V  and  A  when  I  is  constant,  and  combine 

the    two ;    or    (2)    first    find    the    connection    between    the 

y 
apparent  resistance,  _,  and  I  when  A  is  constant,  then  the  con- 

A 
y 

nection  between  —  and  A  when  I  is  constant,  and  combine  the 
A 

two;  or  (3)  start  by  finding  the  relation  between  the  power, 
V  x  A,  and  I  when  A  is  constant,  next  find  the  connection 
between  V  x  A  and  A  when  I  is  constant,  and  combine  the 
two,  &c. 

If  both  the  connections  used  for  any  one  of  these  methods 
followed  straight-line  laws,  it  was  obvious  that  the  equation 
would  be  very  much  easier  to  evolve,  and  the  results  would  be 
more  certain.  It  was  found  that  this  was  the  cise  with  the 
third  method  only,  and  that  was,  therefore,  the  one  employed. 
Plotting  curves  connecting  power  and  length  of  arc  for  various 
constant  currents,  the  series  of  perfectly  straight  lines  seen  in 
Fig.  62,  was  obtained,  and  plotting  curves  connecting  power 


POWER  CURVES.  179 

and  current  for  constant  lengths  of  arc  the  perfectly  straight 
lines  seen  in  Fig.  63  were  obtained. 

In  the  case  of  carbons  the  positive  of  which  was  cored,  it 
was  found  by  the  students  working  under  Prof.  Ayrton  in 
1893  that  the  curves  connecting  power  and  current  for  various 
constant  lengths  of  arc  were  straight  lines  when  the  current 
was  not  less  than  about  5  amperes.  With  the  solid  carbons 
that  I  used,  on  the  other  hand,  these  lines  are  quite  straight 
for  all  currents  —  even  the  smallest  that  I  have  tried,  viz., 
2  amperes. 

As  already  stated,  alnrst  every  point  in  Fig.  61  represents 
the  mean  of  several  results  obtained  at  different  times  with 
different  pairs  of  carbons.  But  the  curves  in  Fig.  61,  having 
been  drawn  through  the  average  position  of  these  mean  points, 
gi\e  still  more  accurately  than  the  points  themselves  the 
ordinate  corresponding  with  any  given  abscissa,  i.e.,  the  number 
of  volts  corresponding  with  any  given  number  of  anperes. 
Hence,  to  obtain  the  number  of  watts  for  each  point  in  Fig.  62, 
points  were  taken  that  were  actually  on  the  curves  in  Fig.  61, 
and  the  number  of  volts  represented  by  their  ordinates  was 
multiplied  by  the  number  of  amperes  represented  by  their 
abscissa).  And  it  is  because  greater  accuracy  was  obtained  in 
this  way  that  the  points  lie  so  well  on  the  straight  lines  in 
Fig.  62.  The  ordinates  of  points  in  Fig.  63  were  taken  direct 
from  the  lines  in  Fig.  62. 

From  Figs.  62  and  63  we  can  ascertain  the  exact  form  of 
the  general  equation 

V=/(A,  0 


connecting  the  P.D.  between  the  carbons  with  any  current  and 
any  apparent  length  of  arc.  For,  in  any  one  of  the  curves  in 
Fig.  62,  let 

I  equal  the  apparent  length  of  the  arc  in  millimetres, 

W  equal  the  power  in  watts  expended  in  sending  a  given 

current  through  an  arc  I  millimetres  long, 
W0  be  the  power   in   watts   that   would  be  expended  in 
sending  the  same  current  through  an  arc  of  Omm.,    as 
shown  by  the  curve,  and 

W7  be  the  power  in  watts  expended  in  sending  the  same 
current  through  an  arc  7mm.  long. 


180 


THE  ELECTRIC  ARC. 
Both  Carbons  Solid. 


200 


150 


100 


2345 
Length  of  Arc  in  Millimetres. 

Fio,  62.^-Power  and  Length    of  Arc  for  Different   Constant   Currents. 
Carbons  :  Positive  llmm.  ;  negative  9mm. 


,  \^m AT?pN. 

'V     0.    THE  \ 

UNIVERSITY  ) 


, 
POWER  AND  LEX  (IT  11  OF  ARC. 

Then,  by  similar  triangles, 


This,  therefore,  is  the  general  equation  to  the  lines  in  Fig.  62. 
To  obtain  the  equation  to  any  particular  line,  W0  and  Wr  must 
be  replaced  by  their  actual  values  in  the  particular  curve. 

To  give  an  instance.  Take  the  equation  to  the  line  for  a 
constant  current  of  6  amperes.  In  this  case 


and  W0  =  245. 

Therefore  we  have, 

W-245  _  40G  -  245 

T~        ~T~ 

_161 
=  ~7~' 
=  23. 

Hence  W  =  245  +  23£  is  the  equation  to  the  line  representing 
the  connection  between  power  in  watts  and  apparent  length  of 
arc  in  millimetres  for  the  constant  current  of  6  amperes. 

Thus,  in  order  to  apply  equation  (1)  to  any  line  in  Fig.  62, 
we  must  know  the  two  constants  for  that  line,  W7  and  W0, 
and,  as  there  are  11  such  lines,  it  would  be  necessary  to 
have  22  constants  for  those  11  lines.  In  order  to  get  the 
complete  equation,  therefore,  we  must  find  some  relation 
between  all  these  constants. 

Now  the  relation  between  W7  with  one  current  and  W7  with 
another  current  is  simply  the  relation  between  power  in  watts 
and  current  in  amperes  for  a  constant  length  of  arc  of  7mm. 
Hence  the  next  thing  to  be  done  is  to  find  the  law  connecting 
power  with  current  for  various  constant  lengths  of  arc.  This 
law,  as  already  explained,  is  strictly  linear  for  solid  carbons, 
and  in  Fig.  63  are  given  the  straight  lines  for  lengths  of  arc 
Omm.  and  7mm. 

The  top  straight  line  in  Fig.  63  for  an  arc  of  constant 
length  of  7mm.  cuts  the  axis  along  which  current  is  measured 
at  a  distance  to  the  left  of  the  zero  point  which  represents 
1-6  amperes. 

Therefore,  calling  A  the  current  in  amperes,  and  using  the 


182 


THE  ELECTRIC  AUG. 


\ 


\ 


POWER  AND  CURRENT.  183 

notation  already  adopted  for  W,  we  have,  by  similar  triangles, 
Wr  the  watts  corresponding  with  a  current  of  14  amperes 
A+~r6  =  14  + 1-6 

_833 

=  1W' 

=  53-397; 
or  Wr  =  53-397A  +  l-6x  53-397, 

=  53-397A  +  S5-435. 
Hence  Wr  =  53'397  A  +  85-435 

is  the  equation  to  the  upper  line  in  Fig.  63. 

Using  the  same  notation  for  the  lower  curve,  and  remarking 
that  it  cuts  the  axis  of  current  at  a  distance  from  the  zero 
point  which  represents  a  current  of  0'3  ampere,  we  have 

W0  _the  watts  corresponding  with  a  current  of  14  amperes 
A  +  03~  14  +  0-3~ 

_556 
~H-3' 

=  38-881  ; 
or  W0  =  38-881  A  +  0-3  x  38-881, 

=  38-881  A +  11-664. 
Hence  W0  -  38-881  A  +  1 1  -664 

is  the  equation  to  the  lower  line  in  Fig.  63. 

Substituting  the  above  values  for  W7  and  W0  in  equation  (1) 
we  have 

W-(38-881A+ 11-664) 
I 

_  53-397  A +  85-435 -(38-881  A +  11-664) 

~T~ 
_14-516A  +  73-771 

~T~ 
=  2-074A  +  10-54. 

Therefore       W  =  38-881  A  +  11-664  + 1  (2-074  A  +  10-54)  .     (2) 

is  the  general  equation  connecting  the  power  expended  in  a 
silent  arc  in  watts,  the  current  flowing  in  amperes,  and  the 
apparent  length  of  the  arc  in  millimetres  for  the  solid  carbons 


184  THE  ELECTRIC  ARC. 

used.  But  W  =  AV,  therefore,  dividing  both  sides  of  the  pre- 
ceding equation  by  A,  and  omitting  the  fifth  significant  figure, 
we  obtain 

V  =  38-88  +  2074Z  +  U'66  +  10'54;    ....    (3) 

A 

This  is  the  equation  which  we  have  been  seeking,  to  the 
family  of  curves  in  Fig.  61,  and  it  enables  us  to  calculate  V, 
the  P.D.  in  volts  that  it  is  necessary  to  maintain  between 
a  pair  of  solid  carbons  of  the  size  and  hardness  that  I 
used,  in  order  that  a  current  of  A  amperes  may  flow  through  a 
silent  arc  whose  apparent  length,  as  measured  on  the  projected 
image,  is  /  millimetres. 

In  order  to  see  how  nearly  this  equation  actually  represents 
the  curves  in  Fig.  61,  I  have  used  it  to  calculate  the  P.D. 
that  should  correspond  with  currents  of  3,  4,  5,  6,  7,  8, 
9,  10,  12,  14  amperes,  and  in  some  cases  with  currents  of  2 
and  16  amperes  for  all  the  arcs  from  1mm.  to  7mm.  in 
length ;  and  in  Table  XXI.  are  given  the  results  of  81  such 
calculations,  as  well  as  the  actual  P.Ds.  taken  from  the  curves 
themselves. 

An  examination  of  this  table  shows  that  58  out  of  the  81 
calculated  values  of  the  P.D.  do  not  differ  by  more  than  0*05 
of  a  volt  from  the  values  of  the  P.D.  taken  from  the  curves, 
while  of  the  remaining  23  values 

8  differ  by  0'05  to  015  volts  from  the  curve  values, 

5  differ  by  0'15  to  0-25  volts  „  „ 

4  differ  by  0-25  to  0-35  volts  „ 

4  differ  by  0-35  to  045  volts 

1  differs  by  0'8  volt 

1  differs  by  1/5  volt  „  ,, 

so  that  only  two  of  the  81  calculated  values  differ  from  the 
curve  values  by  as  much  as  0*5  volt,  and,  since  these  two  values, 
viz.,  one  belonging  to  a  current  of  2  amperes  with  an  arc  of 
1mm.,  and  the  other  to  a  current  of  3  amperes  with  an 
arc  of  7mm,,  are  on  the  steepest  parts  of  the  curves,  the 
wonder  is,  not  that  there  are  two  values  somewhat  wrong,  but 
that  the  agreement  between  the  calculated  and  the  curve 
values  of  the  P.D.  should  be  so  marked  for  all  the  other 
points  even  in  the  steep  parts  of  the  curves.  For  it  must  be 
remembered  that  a  slight  mistake  either  in  the  reading  of  the 


P.D., 


CURRENT  AND  LENGTH  OF  ARC. 

covpoi«dtiHQpgj^cg._!» 


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O  KD  LO  K)  sO  iH  l>  «*  rH  CO  LO   . 

63  cb  vb  LO  «=r  ^t  rb  rb  rb  CNI  63    : 


0  K5  LO  •*  0  ^1  L>  ^J-  rH  0  CJ 

o  do  o  LO  <;t  •=!•  rb  K>  K)  6a  6a 

LO«3-5T 


185 


186  THE  ELECTRIC  ARC. 

current  or  of  the  length  of  the  arc  makes  a  large  error  in  the 
P.D.  when  the  current  is  small. 

There  can  be  no  doubt,  then,  that  equation  (3)  accurately 
gives  the  law  connecting  P.D.  current,  and  apparent  length  of 
arc  for  solid  carbons  of  the  size  and  hardness  that  I  have  used. 

The  general  form  of  this  equation  is 


(4) 
which  may  be  written 


Now  this  is  the  equation  to  a  rectangular  hyperbola  when  I  is 
constant,  and  the  asymptotes  are  —  one  the  axis  along  which 
P.D.  is  measured,  the  other  a  line  parallel  to  the  axis  along 
which  current  is  measured.  Hence  the  curves  in  Fig.  61  are 
a  series  of  rectangular  hyperbolas,  having  one  asymptote  in 
common,  which  is  used  as  the  axis  of  P.D.,  while  their  other 
asymptotes  are  lines  parallel  to  the  axis  of  current  and  at  a 
distance  from  it  depending  upon  the  value  of  I.  In  fact,  if  d 
be  the  distance  of  the  asymptote  of  any  one  of  the  curves  from 
the  axis  of  current,  then 


or  d  =  38-88  +  2-074  Z, 

where  I  stands  for  the  number  of  millimetres  in  the  length  of 
the  arc,  and  the  unit  of  length  for  d  is  the  length  that  has 
been  arbitrarily  taken  to  represent  a  volt  in  drawing  the  curves 
in  Fig.  61. 

These  curves  have  not  the  appearance  of  rectangular  hyper- 
bolas, but  that  arises  from  different  units  of  length  having 
been  taken  to  represent  a  volt  and  an  ampere.  In  Fig.  64  I 
have  therefore  redrawn  the  particular  curve  in  Fig.  61  which 
corresponds  with  a  constant  length  of  arc  of  5mm.,  and,  since 
'  the  same  length  has  been  taken  to  represent  a  volt  and  an 
ampere  in  Fig.  64,  the  identity  of  the  curve  in  this  figure  with 
a  rectangular  hyperbola  becomes  evident.  The  asymptotes, 
the  axis,  and  the  focus  of  this  rectangular  hyperbola  are  also 
indicated. 

The  law  embodied  in  equation  (4)  connecting  the  P.D. 
between  the  carbons  with  the  length  of  the  arc  and  the  current 
flowing  has  been  proved  to  be  true  for  the  solid  carbons  I  used 


P.D.  CURRENT,  AND  LENGTH  OF  AUG.          18 
Both  Carbons  Solid. 


82 
SO 

78 

76 
74 

72 

70 

3 
^  68 

I6' 

5  64 
1 

Cj 

a;  62 

60 

58 
56 
54 
52 

50 
0 
0 

1 

\ 

/ 

/ 

/ 

ymptote. 

\ 

/ 

/ 

"< 

\ 

/ 

/ 

\ 

/F 

/ 

\ 

/ 

/ 

\ 

/ 

\ 

/ 

/ 

X 

. 

/ 

/ 

^^ 

"^  — 

—  —  —  ^ 

/ 

/ 

Asyrr 

ptote. 

2             4             6             8             10           12           14           16           18          20 

Current  in  Amperes. 

FIG.  64. — Hyperbola  showing  connection  between  P.D.  and  Current  for 
constant  Length  of  Arc  of  5mm.,  when  Volts  and  Amperes  are  drawn  to 
the  same  scale.  O  M,  0  N  are  the  two  asymptotes,  0  F  the  axis,  and 
F  the  focus  of  the  hyperbola. 


188  THE  ELECTEIG  ARC. 

(it  cannot  be  too  carefully  borne  in  mind  that  this  law  does 
not  apply  to  cored  carbons) ;  but  before  it  can  be  accepted  as 
a  universal  law,  it  must  be  shown  to  apply  to  the  results 
obtained  by  other  experimenters  with  solid  carbons. 

In  their  Paper  published  in  the  American  Electrical  Engineer 
for  August  2,  1893,  of  which  an  abstract  is  given  on  p.  66, 
Messrs.  Duncan,  Rowland  and  Todd,  after  quoting — not  quite 
correctly — the  equations  employed  by  various  experimenters  to 
connect  the  P.  D.  between  the  carbons  with  the  current  flowing  and 
the  length  of  the  arc,  said  :  "  In  fact,  almost  any  results  may  be 
obtained  by  modifying  the  size  and  composition  of  the  carbons." 
I  shall  show,  however,  from  the  results  of  the  very  experimenters 
whose  equations  they  quoted  that  this  is  not  the  case,  and  that 
the  form  of  the  true  equation  connecting  these  variables  is  the 
same  whatever  the  size  of  the  carbons  may  be,  and  whatever 
their  composition,  as  long  as  the  carbons  are  solid.  The  values 
of  the  constants  in  the  equation  does,  however,  depend  on  the 
hardness  of  the  carbons,  and  perhaps  on  their  size. 

It  will  be  found,  also,  that  although  in  certain  eases  my 
equation  does  not  support  the  conclusions  arrived  at  by  pre- 
vious experimenters,  it  is  really  more  in  accordance  with  the 
results  of  tkiir  oivn  experiments  than  were  the  conclusions  they 
themselves  deduced  from  them. 

If  we  take  equation  (2) 

W  =  38-88  A+  11-66  +  (2-074  A  +  10-54)  I. 

A  10-54  .    ., 

and  put          A  =   -  _--  in  it, 

wehave          W=  38*88  x  (-  ~5—\  +  11  66, 

that  is,  we  have  a  value  for  A,  and  a  corresponding  one  for  W, 
both  of  which  are  independent  of  the  value  of  I,  showing  that 
all  the  lines  connecting  A  and  W  for  the  various  constant 
lengths  of  arc  must  pass  through  one  point,  the  co-ordinates  of 
which  are 

2-074 

and  W  =  38-88  x  f  -  L-|4)  +  11-66; 

or,  A  =  -  5-08 

and  W=- 185-92. 


POWER  LAWS.  189 

00.  00 

Similarly,  by  putting  I  =  -          -9  the  coefficient  of  A  dis- 


appears in  the  same  equation,  and  we  find  that  all  the  lines 
connecting  W  and  I  for  the  various  constant  currents  must  pass 
through  a  point,  the  co-ordinates  of  which  are 

1=  -187, 
W=  -185-92. 

Hence  the  laws  upon  which  equation  (4)  is  founded,  and 
upon  which  it  depends  absolutely,  may  be  put  in  the  following 
form  :  — 

1.  When  the  current  is  constant,  a  straight-line  law  connects 
the  power  consumed  in  the  arc  with  the  length  of  the  arc. 

2.  When  the  length  of  the  arc  is  constant,  a  straight  line 
law  connects  the  power  consumed  in  the  arc  with  the  current 
flowing. 

3.  The  straight  lines  representing  the  connection  between 
power  and  length  of  arc  for  constant  currents  all  meet  at  a 
point. 

4.  The  straight  lines  representing  the  connection  between 
power  and  current  for  constant  lengths  of  arc  all  meet  at  a 
point. 

The  first  of  these  four  laws  follows  directly  from  Edlund's 
law,  that,  with  a  constant  current,  the  apparent  resistance  of  the 
arc  is  equal  to  a  constant  part  plus  a  part  that  varies  with  the 
length  of  the  arc.  The  other  three  have  not  hitherto  been 
enunciated,  but  it  will  be  seen  that  the  whole  four  laws  are 
true  for  the  results  of  all  the  experiments  made  with  solid 
carbons  of  which  detailed  information  regarding  the  numbers 
has  been  published. 

Edlund  gave  only  the  ratios  of  the  currents  he  used,  so  that 
it  would  not  be  possible  to  construct  a  complete  equation, 
including  all  three  variables  from  his  results  ;  but  the  equation 
he  discovered,  r  =  a-t-bl  for  constant  currents,  is,  as  stated 
above,  really  another  form  of  the  first  law  I  used,  for  if  we 
multiply  this  equation  throughout  by  the  constant  A2  we 
obtain  an  equation  of  the  form 


a  linear  equation  connecting  W  and  I  for  constant  currents. 


190 


THE  ELECTRIC  ARC. 


The  resistance  form  of  my  equation  (3)  is 
38-88  +  2-074  Z  ,  11  6 


:,    .    •    (5) 


A  A2 

and  making  A  constant  in  this,  we  get  an  equation  of  the  form 


where 


and 


=  38-88     11-66 
~~      ~~ 


2-074  ^10-54 
T~        A2   ' 


Now  Edlund  concluded  from  the  results  of  his  experiments  that 
a  and  b  both  diminished  as  the  current  increased,  and  this  is 
borne  out  by  the  above  values  for  a  and  b'}  but  he  also  thought 
that  a  varied  inversely  as  the  current,  which  although  not  exactly 
correct,  was  nearly  so  for  all  but  small  currents,  for  unless  A  were 

very  small  in  the  above  value  for  a,  the  term would  be 

,     ...    38-88  A'2 

small  compared  with -. 

A 

Further,  that  the  values  which  Edlund  found  for  a  A  were 
not  constant,  as  they  would  be  if  a  varied  inversely  as  A,  but 
in  every  instance  but  one  showed  a  decrease  as  the  current 
increased,  is  very  easily  seen  from  the  following  table,  which 
gives  the  results  Edlund  obtained  from  his  experiments  with 
arcs  between  carbon  electrodes  : — 

Table  XXII.— Results  obtained  ly  Edlund. 


Numbers  proportional 
to  A. 

Numbers  proportional 
to  a  A. 

Series  of 
experiments. 

1-2387 
1-0176 
0-6661 

0-3239 
0-3416 
0-3336 

1 

5> 

1-1139 

0-9435 

6-69 
6-877 

2 

0-9618 
0-7738 

6-34 
6-48 

6 

5J 

1-3270 
0-9827 

4-45 
521 

4 

The  experiments  of  one  series  must  not  be  compared  with 
those  of  another,  for  each  was   carried   out   under   different 


EDLUND.  191 

circumstances.  But  a  comparison  of  those  in  each  series  will 
show  that,  except  for  one  in  the  first  series,  the  product  a  A 
increases  as  the  current  A  diminishes,  which  is  exactly  what 
would  follow  from  my  value  of  a  A,  viz.  :  — 


A 

Hence  deviations  which  Edlund  mistook  for  errors  of  observa" 
tion  were  evidently  caused  by  the  presence  of  the  term 

-i  -j  t  /»  /» 

corresponding    with     -   in   the    value   of   a  A,   and    what 
A 

Edlund  did  not  notice  was  that  with  one  exception  all  his 
errors  were  in  the  same  direction.  Thus  the  conclusion  to  be 
drawn  from  my  equation  (4)  with  regard  to  a  A,  which  Edlund 
called  the  back  E.M.F.  of  the  arc,  is  more  in  harmony  with 
the  results  of  his  experiments  than  his  own  conclusion  was. 

It  is  hardly  necessary  to  enter  into  Edlund's  theoretical 
reasons  for  supposing  the  term  a  A  to  be  independent  of  the 
current,  since  his  own  results  really  proved  that  it  was  not  so. 

To  show  the  fallacy  of  his  theory  that,  with  a  generator  of 
constant  E.M.F.,  the  total  power  expended  in  the  arc  was 
proportional  to  the  current,  I  need  only  point  out  that,  if  it 
were  so,  A  V  would  be  equal  to  k  A,  where  k  is  a  constant,  or 
V  would  be  a  constant  for  all  currents. 

In  the  experiments  used  by  Frolich  there  was  no  sort  of 
order.  Only  in  two  cases  were  more  than  two  currents  em- 
ployed with  the  same  length  of  arc,  and  in  no  case  was  the 
same  current  used  with  more  than  two  lengths  of  arc  ;  thus  it  is 
impossible  to  construct  a  complete  equation  from  them.  Fortu- 
nately, however,  several  currents  were  used  with  an  arc  of  2mm., 
and  by  calculating  the  power  expended,  from  the  numbers  given 
for  currents  and  P.Ds.,  it  is  possible  to  plot  the  curve  connecting 
watts  and  amperes  for  length  of  arc  2mm.,  and  this  proves  to  be 
a  straight  line,  as  it  should  be  according  to  the  second  law 
upon  which  my  equation  is  founded. 

The  equation  to  this  straight  line  obtained  from  the  experi- 
ments used  by  Frolich  was 


from  which  we  get  the  P.D.  in  volts, 
V.  40-25 


A 


192  THE  ELECTRIC  ARC. 

Table  XXIII.  shows  the  value  of  the  P.D.  for  each  current 
quoted  by  Frolich  for  the  2mm.  arc,  and  the  value  calculated 
from  the  preceding  equation. 

Table  XXIII. — Results  used  by  Frolich. 


Current  in  amperes. 

P.D.  from  experiment. 

P.D.  from  equation. 

27-4 

42-7 

42-75 

11-6 

46-3 

46-13 

8-39 

50-1 

48-38 

7-67 

47-1 

4915 

6-92 

501 

5011 

The  general  agreement  of  the  values  for  V  obtained  by 
experiment  and  calculation  is  striking,  considering  that  different 
pairs  of  carbons  were  used  by  different  people  in  obtaining  the 
experimental  results,  and  this  agreement  renders  it  quite 
certain  that  V  and  A  are  connected  by  an  equation  of  the  form 
I  have  given. 

Frolich's  statement,  therefore,  that  the  P.D.  between  the 
carbons  was  independent  of  the  current,  and  that  the  true 
equation  was 

V  =  m  +  n  I, 

where  m  and  n  were  constant  for  all  currents,  is  indeed 
astonishing,  and  still  more  so  is  the  fact  of  his  having  given 
values  for  m  and  n  —  viz.,  39  and  1'8,  and  having  asserted  that 
the  equation 


was  true  for  all  currents  up  to  100  amperes.  For,  to  take 
only  the  numbers  given  in  Table  XXIIL,  which  are  for  length 
of  arc  2mm.,  his  formula  would  give 

V  =  42  -6  volts 

for  all  the  currents,  whereas  42-7  volts  is  the  smallest  P.D.  for 
the  largest  current,  and  the  P.D.  for  the  smallest  current  is 
50  volts,  or  7J  volts  greater  than  the  P.D.  as  calculated  by 
Frolich.  Such  discrepancies  as  these,  however,  he  dismissed 
as  errors  of  observation,  and  he,  like  Edlund,  did  not  notice 
that  all  or  nearly  all  these  apparent  errors  of  observation 
were  in  the  same  direction. 

Since  Frolich's  equation  did  not  really  express  the  results  of 
the  experiments  upon  which  he  founded  it,  it  is  unnecessary 


PEUKERT.  195 

to  dwell  upon  the  other  equations  which  he  deduced  from  it, 
and  which  were  equally  at  variance  with  the  experimental 
results.  Indeed,  the  only  suggestion  made  by  Frolich  in  his 
Paper  that  appears  likely  to  prove  true  was  that  the  cross- 
section  of  the  arc  was  directly  proportional  to  the  current. 

The  first  systematic  attempt  to  find  the  P.Ds.  that  would 
send  a  given  constant  current  through  many  lengths  of  arc 
was  made  by  Peukert,  who  first,  after  Edlund,  saw  the  value  of 
eliminating  one  of  the  three  variables,  P.D.,  current  and  length 
of  arc  in  his  experiments. 

Having  measured  the  P.Ds.  corresponding  with  various 
currents  and  lengths  of  arc,  Peukert  plotted  curves  connecting 
apparent  resistance  and  length  of  arc,  and  found  them  to  be 
straight  lines.  He  gave  the  equations  to  these  lines,  and  from 
them  I  have  constructed  the  following  equations  connecting 
power  and  length  of  arc  for  each  of  the  currents  he  used,  by 
multiplying  each  equation  through  by  the  square  of  the  current 
which  corresponded  with  it : — 

For  A  =  10  amperes,  W  =  366  +  23  I. 
„    A=15        „         W  =  517  +  33-75J. 

„    A  =  20        „         W  =  720  +  32/. 

„    A  =  25        „         W-812-3  +  46-87J. 

These,  when  plotted,  give  the  four  straight  lines  seen  in 
Fig.  65,  and  thus  it  is  evident  that  Peukert's  results  follow  the 
first  of  the  four  laws  enunciated  on  p.  189.  It  is  clear  that  the 
line  for  20  amperes  is  wrong  for  it  does  not  make  a  large 
enough  angle  with  the  axis  of  I,  hence  the  coefficient  of  J, 
which  determines  the  slope  of  the  line,  must  be  too  small  in 
the  power  equation  for  20  amperes.  That  that  is  the  case  is  seen 
from  an  examination  of  these  four  power  equations,  for  while 
the  coefficients  of  I  with  10,  15  and  25  amperes  increase  as 
the  current  increases,  that  with  20  amperes — viz.,  32 — is  less 
than  3375,  the  coefficient  with  15  amperes. 

If  from  the  four  lines  connecting  power  and  length  of  arc 
for  each  current  we  take  the  number  of  watts  corresponding 
with  length  of  arc  10mm.,  and  plot  them  as  ordinates  with 
their  respective  currents  as  abscissae,  we  shall  obtain  a  curve 
representing  the  connection  between  the  power  absorbed  in  the 
arc  and  the  current  flowing  when  the  length  of  the  arc  is  kept 


194 


THE  ELECTEIC  ARC. 


constant  at  10mm.     Similar  lines  may  be  obtained  in  the  same 
way  for  all  the  other  lengths  of  arc  down  to  Omm.     These  lines, 


From  Peukert's  Experiments. 


1600 


1500 


1400 


1300 


1200 


1100 


1000 


900 


700 


600 


500 


400 


4  6  8  10  12 

Length  of  Arc  in  Millimetres. 


16 


Fia.r65.  —  Power  and  Length  of  Arc  for  Different  Constant  Currents. 


PEUKEET.  195 

of  which  those  for  10mm.  and  Omm.  are  given  in  Fig.  66,  are  all 
straight  Lines  showing  that  Peukert's  results  follow  the  second 
law  given  on  p.  189,  namely  that  with  a  conatant  length  of  arc 
the  connection  between  the  power  absorbed  in  the  arc  and  the 
current  flowing  follows  a  straight  line  law. 
The  equations  to  these  lines  are 

W10  =  46-22  A  +  129-42, 
W0  =  30A  +  66. 

Substituting  these  values  for  W10  and  W0  in 
W-W0_W10-W0 

/  10 

which  is  the  equation  to  any  one  of  the  lines  in  Fig.  65  con- 
necting power  with  length  of  arc  for  a  constant  cm-rent,  we  find 
the  equation 

W  =  30  A  +  66  +  (1-622  A  +  6-342)  I, 

representing  the  connection  between  power,  length  of  arc  and 
current,  when  all  three  may  vary. 

Dividing  throughout  by  A,  we  have  — 


A 

which  is  the  general  equation  representing  the  connection  be- 
tween the  P.D.  between  the  carbons,  the  current  flowing  and 
the  length  of  the  arc  with  the  solid  carbons  used  by  Peukert. 

In  order  to  test  how  nearly  the  equation  given  above  really 
expresses  Peukert's  results,  we  may  divide  by  A,  and  obtain  the 
equation  for  the  apparent  resistance  of  the  arc  :  — 
30  +  1-622?     66  +  6-3421 
A  ~^2— 

If  we  now  give  A  the  values  respectively  of  10,  15,  20  and 
25  amperes  in  this  resistance  equation,  we  find  the  equations 
on  the  right-hand  side  of  Table  XXIV.  :— 

Table  XXIV.  —  From  Peukert's  Results. 


Current  in  amperes. 

Peukert's  equations. 

From  the  above  general 
equation. 

10 
15 
20 
25 

r  =  3-66  +  0-23  1 
r  =  2-3  +0-151 
r=l-Q   +  Q-G81 
r  =  l-3   +  0-075  1 

?•  =  3-66  +  0-23  1 
r  =2-29  +  0-14  1 
r  =  1-67  +  0-096  1 
r  =  1-31  +  0-075  1 

o2 


196 


THE  ELECTRIC  ARC. 


\ 


\ 


Q> 

£ 
'£ 
o 
a 
x 

UJ 

CO 

t 

o 


\\ 


\ 


PEUKEET.  197 

Comparing  the  two  sets  of  equations,  we  find  a  striking 
agreement  in  the  case  of  the  first,  second  and  fourth  equations, 
while  the  third,  which  differs  from  that  given  by  Peukert, 
expresses  the  result  which  Peukert  would  have  obtained  if  he 
had  not,  as  already  explained,  made  an  error  when  testing  with 
20  amperes. 

Thus  it  is  apparent  that  the  results  of  Peukert's  experiments 
lead  to  an  equation  of  exactly  the  same  form  as  my  equation 
(4),  differing  from  it  only  in  its  constants,  hence  his  results  must 
not  only  follow  the  two  first  laws  upon  which  equation  (4)  was 
founded,  but  they  must  also  follow  the  last  two.  That  this 
is  so  is  easily  seen, 

for,  if  we  put  A  =  -  in  the  power  equation  for  Peukert's 

J.  'bLilj 

results,  the  coefficient  of  I  disappears,  and  we  have 
W-68-80xgg. 

Hence  A=  -3-91 

and  W=-51-3 

are  the  co-ordinates  of  a  point  where  all  the  lines   connecting 

power  and  current  for  the  various  constant  lengths  of  arc  must 

meet. 

30 
Similarly  putting  I  =  -  ,  the  coefficient  of  A  disappears, 

and  we  get 

1=  -18-5 

and  W=-51-3 

as  the  co-ordinates  of  a  point  at  which  all  the  lines  connecting 
power  and  length  of  arc  for  the  various  constant  currents  must 
meet. 

Thus  the  results  of  Peukert's  experiments  completely  fulfil 
all  the  four  laws  upon  which  my  equation  (4)  is  founded  and 
are,  therefore,  completely  in  harmony  with  my  results.  It  is 
easy  to  show  that  where  the  conclusions  he  drew  differ  from 
mine,  his  own  experiments  prove  him  to  have  been  mistaken. 

The  resistance  form  of  the  general  equation  deduced  above 
from  Peukert's  results  may  be  put  in  the  form 
r  =  a  +  b  I, 

30     66 

where  a  =  —  +  — 

A     A2 

,      1-622     6-342 
and  6=_+_. 


198  THE  ELECTRIC  ARC. 

The  second  term  in  the  value  for  a  is  never  very  big  compared 
with  the  first  term,  with  the  currents  Peukert  used,  for  the 
numerator  of  the  second  term  is  only  about  twice  as  great  as  the 
numerator  of  the  first,  whereas  the  denominator  of  the  second  is 
at  least  ten  times  as  great  as  the  denominator  of  the  first,  since 
the  smallest  current  Peukert  used  was  one  of  10  amperes. 
Hence  it  is  not  very  surprising  that  Peukert  followed  Edlund 
in  considering  that  the  variations  in  the  value  of  a  caused 
by  the  presence  of  this  term  were  due  to  errors  of  observation, 
and  in  asserting  that  a  varied  inversely  as  the  current.  Yet 
his  own  results  show  that  this  is  not  the  case,  for  if  it  were, 
a  A  would  be  a  constant,  whereas  multiplying  the  first  term 
in  each  of  Peukert's  own  equations  by  the  corresponding 
current,  the  resulting  numbers  are  36-6,  34-5,  36,  and  32*5, 
which,  except  in  the  case  of  the  equation  for  20  amperes, 
which  I  have  already  shown  to  be  wrong,  go  in  descending 
order  as  the  current  increases,  as  my  equation  indicates  that 
they  should.  He  saw,  however,  that  b  diminished  more  rapidly 
than  the  current,  and  this  he  was  able  to  do  because,  on 
examining  the  expression  I  have  given  above  for  6,  we  see  that 
the  coefficient  of  the  second  term  is  four  times  as  great  as  that 
of  the  first  term.  Hence  even  with  fairly  large  currents  the 
second  term  is  not  negligible  compared  with  the  first,  and 
consequently  Peukert  was  able  to  find  an  approximate  law  for 
the  value  of  6,  for  which  the  last  equation  gives  the  full  and 
exact  law. 

From  the  experimental  observations  published  by  Messrs. 
Cross  and  Shepard  I  have  plotted  curves  connecting  the 
apparent  resistance  and  length  of  the  silent  arc  for  each 
current  they  used,  and  have  found  an  equation  to  each  of 
these  lines  which  fits  their  results  rather  more  closely  than 
those  which  they  themselves  gave.  From  these  slightly  more 
accurate  equations  I  constructed  the  following  equations  con- 
necting power  and  length  of  arc,  by  multiplying  each  equation 
by  the  square  of  the  corresponding  current, 

For  A  =  5-04  amperes,  W  =  201-31  +  3-34  I 
„    A  =  7-0         „        W  =  273-01+3-6Z 
„     A  =  7-92       „        W  =  310-01+  6-24 1 
A  =  10-04  W  =  380-01  +  8-94  I 


CROSS  AND  SHEPAED. 


199 


These,  when  plotted,  give  the  straight  lines  in  Fig.  67, 
showing  that  Cross  and  Shepard's  results  follow  the  first  law 
on  p.  189.  As  with  Peukert's  curves,  one  line — the  line  for 
7  amperes — has  the  wrong  slope,  as  may  also  be  seen  from  the 
power  equations.  For  evidently  the  coefficient  of  I  for 
7  amperes  is  too  near  in  value  to  the  coefficient  for  5 -04 
amperes,  and  not  near  enough  to  that  for  7 '9  2  amperes. 

From  Cross  &  Shepard's  Experiments. 


500 


400 


200 


^ 


12 


14 


0  2  4  6  8  10 

Length  of  Are  in  Thirty-seconds  of  an  Inch. 
FIG.  67.—  Power  and  Length  of  Arc  for  Different  Constant  Currents. 

Taking  the  number  of  watts  corresponding  with  length  of 
arc  10  from  each  of  the  four  lines  in  Fig.  67,  and  plotting  them 


200 


THE  ELECTRIC  ARC. 


with  their  respective  currents,  we  obtain  the  upper  line  in 
Fig.  68,  and  plotting  the  watts  for  length  of  arc  0  with  their 
corresponding  currents,  we  get  the  lower  line. 

That  these  are  straight  lines  is  very  evident,  although  one 
point  of  each  is  off  the  line,  and  it  is  thus  evident  that  Cross 
and  Shepard's  results,  as  well  as  Peukert's,  follow  the  second  of 
the  four  laws  on  p.  189. 

From  Cross  &  Shepard's  Experiments. 


500 
400 
300 
200 
100 


89 


0123466 
Current  in  Amperes. 

Fia.  68. — Power  and  Current  for  Arcs  of  10  thirty-seconds  of  an 
inch  and  0  thirty-seconds  of  an  inch. 

The  equations  to  the  two  lines  in  Fig.  68  are 
W10  =  48A  +  93-6, 
W0  =  37A  +  14'8. 

Substituting  these  values  for  W10  and  W0  in  the  equation 

W-W0_W10-W0 


10   11 


I 


10 


which  is  the  equation  to  any  one  of  the  lines  in  Fig.  67,  we 
have 


as  the  general  equation  connecting  the  power,  current  and 
length  of  arc,  when  any  of  the  three  may  vary,  with  the 
carbons  used  by  Cross  and  Shepard. 

Dividing  by  A  we  have 


CEOSS  AND  SHEPARD. 


201 


as  the  general   equation  connecting  P.O.,  length  of  arc  and 
current  for  the  Cross  and  Shepard  results. 

If  now  we  divide  this  last  equation  throughout  by  A  we  get 


37     14*     /l-l     7j88\ 
A       A2       \T"  1*7 


for  the  resistance  equation,  and  giving  A  the  values  of  the 
currents  used  in  the  experiments,  we  get  the  equations  on  the 
right-hand  side  of  the  following  table  : — 

Table  XXV. — From  Cross  and  Shepard's  Results. 


Current  in  amperes. 

From  experiments. 

From  general  equation. 

5-04 
7-0 
7-92 
10-04 

r  =  7-925  +  0-525  1 
r  =  5'57   +  0-277  1 
r  =  4-94   +  0-259  1 
r  =  3'77   +  0188  1 

r  =7-923  +  0-528  1 
r  =  5'59  +  0-317  1 
r=4'91    +  0-264  1 
r  =  3'83  +  0-187Z 

The  two  sets  of  equations  agree  very  nearly  as  well  as  those 
obtained  from  Peukert's  results,  although  the  range  of  current 
was  so  much  smaller,  and  the  exact  course  of  the  lines  was, 
therefore,  much  more  difficult  to  obtain.  This  closeness  of 
agreement  shows  that  my  general  equation  gives  the  con- 
nection between  the  three  variables  in  the  case  of  Cross  and 
Shepard's  experiments,  as  it  does  with  Peukert's. 

The  co-ordinates  of  the  point  at  which  the  lines  in  Fig.  67 
meet  may  be  found  in  the  same  way  as  similar  co-ordinates 
have  been  found  previously.  They  are — 


and 


/=  -33-64 
W=  -250-12, 


Similarly,  the  co-ordinates  of  the  point  at  which  the  lines  in 
Fig.  68  meet  are 


and 


A=  -7-16 
W=  -250-12. 


Thus,  Messrs.  Cross  and  Shepard's  results  follow  the  four 
laws  upon  which  my  equation  is  founded. 

Besides  calculating  the  values  of  the  constants  a  and  b  in  the 
resistance  equation  r  =  a  +  bl,  Messrs.  Cross  and  Shepard  gave 


202  THE  ELECTEIG  AEC. 

the  value  of  the  product  a  A  for  each  of  the  currents  used. 
As  already  mentioned,  Edlund,  Frolich  and  Peukert  had  con- 
sidered that  this  product  was  on  the  whole  a  constant,  and  this 
constancy  Edlund  regarded  as  proving  the  existence  of  a  constant 
back  E.M.F.  in  the  arc.  Messrs.  Cross  and  Shepard,  however, 
showed  that  the  product  diminished  as  the  current  increased  ; 
they  did  not  give  the  actual  law  of  variation,  which,  in  my 
remarks  on  Peukert's  equations,  I  have  pointed  out  is 

A  constant 

a  A  =  constant  +  -  ; 
A 

but  to  them  is  due  the  credit  of  first  noticing  that  as  A 
increased  a  A  diminished,  and  also  of  pointing  out  that 
Peukert's  equations,  when  correctly  interpreted,  led  to  the 
same  conclusion. 

The  formula  given  by  Prof.  Silvanus  Thompson  in  1892, 

V  =  m  +  n  —  , 

A 

where  m  might  vary  from  35  to  39  volts,  and  n  might  have 
values  from  8  to  18,  was  the  first  real  attempt  to  find  one 
equation  connecting  the  P.D.,  current  and  length  of  the  arc 
when  all  three  varied. 

Multiplying   his  equation   throughout   by  A,  we   have  the 
equation  for  the  power 


which  gives  straight  lines  for  power  and  length  of  arc  with  con- 
stant currents,  and  straight  lines  for  power  and  current  with 
constant  lengths  of  arc,  following  the  two  first  laws  on  p.  189  ; 
but  as  he  did  not  know  the  law  of  variation  of  the  coefficients 
m  and  n,  nor  what  their  variation  depended  upon,  his  equation 
was  necessarily  incomplete. 

At  the  meeting  of  the  British  Association  at  Ipswich  in 
1895,  Prof.  Thompson  stated  that  his  equation  was  founded 
on  experiments  made  by  different  students  at  different  times, 
with  different  carbons,  and  with  different  currents  produced  by 
different  generators,  and  that  the  variations  of  m  and  n  in  it 
appeared  to  depend  upon  some  of  these  differences,  but  he 
could  not  quite  tell  which. 


DUNCAN,  ROWLAND  AND  TODD.  203 

The  Paper  by  Messrs.  Duncan,  Rowland  and  Todd,  from 
which  I  have  already  quoted,  begins  with  a  list  of  the  equations 
used  by  other  experimenters,  among  them 


attributed  to  Edlund,  and 


attributed  to  Cross  and  Shepard. 

What  Edlund,  and  also  Cross  and  Shepard,  really  proved, 
however,  was  that  for  any  particular  value  of  the  current  the 
equation  connecting  the  apparent  resistance  of  the  arc  with  the 
length  was 

r  —  a  +  bl, 

•where  a  and  b  were  constants  for  the  particular  current.  But 
\vhen  the  current  was  increased  they  showed  that  a  and  b  both 
diminished  ;  therefore,  while  it  is  perfectly  correct  to  add 
together  C&J  Ax  and  bl  AJ  l},  in  order  to  find  Vj,  the  P.D.  between 
the  carbons  for  a  length  ^  and  for  a  current  A15  for  which  the 
values  of  a  and  b  are  a^  and  bv  it  is  entirely  wrong  to  attribute 
to  Edlund,  or  to  Cross  and  Shepard,  as  Messrs.  Duncan,  Rowland 
and  Todd  have  done,  the  general  equation 


where  a  and  b  appear  to  be  constant  for  all  values  of  A  and 
of  I 

It  seems  to  be  desirable  to  draw  attention  to  this  correc- 
tion, because  the  versions  of  Edlund's  and  of  Cross  and  Shepard's 
equations  given  by  Messrs.  Duncan,  Rowland  and  Todd  have 
been  subsequently  quoted  as  correct  by  others,  who  have,  I 
presume,  not  referred  to  the  original  publications. 

Messrs.  Duncan,  Rowland  and  Todd  gave  the  values  of  the 
P.D.  and  current  obtained  experimentally  for  one  length  of  arc 
•Jin.  long  obtained  with  cored  carbons.  On  calculating  from 
these  the  values  of  the  power,  I  find  that  the  curve  connecting 
power  and  current  is  very  nearly  a  straight  line,  and  therefore 
very  nearly  fulfils  my  second  law.  I  have  before  mentioned 
that  for  cored  carbons  the  curve  connecting  power  and  current 
was  only  almost  a  straight  line. 


204 


THE  ELECTRIC  ARC. 


The    equation  to  the  straight  line   obtained  from  Duncan 
Rowland  and  Todd's  experiments  is 


therefore  for  the  P.D.  we  have 


In  Table  XXVI.  is  given  a  comparison  of  the  values  of  the 
P.D.  obtained  experimentally  by  Messrs.  Duncan,  Rowland  and 
Todd,  and  the  values  calculated  from  the  preceding  equation. 

Table  XXVI.  —  From  Duncan,  Roivland  and  Todd's  Results. 


P.D.  in  volts. 

From  experiment. 

From  the  equation. 

3-1 

65'0 

67-8 

4-6 

58-5 

58-9 

615 

54-8 

54-3 

7-7 

52-5 

51-5 

8-0 

52-0 

611 

9-82 

49-2 

49-2 

11-26 

47-5 

48-1 

12-75 

46-5 

47-2 

It  is,  of  course,  impossible  to  tell  from  the  table  given 
whether  the  first  law  connecting  power  and  length  of  arc  for 
constant  currents  is  borne  out  by  Duncan,  Rowland  and  Todd's 
results,  for  they  only  gave  the  results  for  one  length  of  arc.  In 
any  case,  however,  it  was  amply  proved  by  the  experiments 
of  Prof.  Ayrton's  students  with  cored  carbons,  that  the  curve 
representing  the  connection  between  power  and  length  of 
arc  for  constant  current  is  not  a  straight  line  for  cored 
carbons. 

Messrs.  Duncan,  Rowland  and  Todd  gave  as  the  equation 
connecting  V,  I  and  A, 


but,  as  the  form  of  the  functions  was  not  stated,  it  is,  of  course, 
impossible  to  make  a  comparison  between  that  equation  and 
the  one  at  which  I  have  arrived. 

To  sum  up,  then,  it  appears  that  wherever  experimenters 
using   solid  carbons  have    given  the   actual  results  of   their 


SUMMARY.  205 

experiments  in  numbers,  the  law  of  those  numbers  can  be 
expressed  with  remarkable  accuracy  by  an  equation  of  the 
same  form  as  mine 


A 

and  differing  from  it  only  in  the  values  of  the  constants  a,  b, 
c  and  d.  Hence,  so  far  from  the  different  experimenters  on 
the  arc  having  all  obtained  different  laws,  as  has  hitherto 
been  supposed,  their  results  present  a  striking  unanimity  when 
viewed  by  the  light  of  the  wider  generalisations  in  which  they 
have  now  been  presented. 


SUMMARY. 

I.  With   solid   carbons,   when   the   current   is   constant,   a 
straight  line  law  connects  the  power  consumed  in  the  arc  with 
its  length,  and  the  several  lines  showing  this  connection  for    ' 
given  carbons,  all  meet  at  a  point. 

II.  With   solid    carbons,    when   the    length    of   the    arc    is 
constant,  a  straight  line  law  connects  the  power  consumed  in 
the  arc  with  the  current,  and  the  lines  showing  this  connection 
for  given  carbons  also  meet  at  a  point. 

III.  The  equation  representing  the  connection  between  the 
P.D.  between  the  carbons,  the  current,  and  the  length  of  the 
arc,  with  solid  carbons,  is 


where  a,  b,  c,  and  d  are  constants  depending  only  upon  the 
carbons  employed. 

IV.  This  is  the  equation  to  a  series  of  rectangular  hyper- 
bolas having  the  axis  of  P.D.  for  one  asymptote,  and  a  line 
parallel  to  the  axis  of  current  at  a  distance  from  it  depending 
on  the  length  of  the  arc  only,  for  the  other. 

V.  The  results  of  experiments  made  by  Edlund,  Frolich, 
Peukert,  and  Cross  and  Shepard  all   give  equations  of   the 
same  form  as  the  above. 


CHAPTER  VII. 


THE    P.D.    BETWEEN    THE     POSITIVE     CARBON    AND     THE    ARC. 

THE  FALL  OF  POTENTIAL  THROUGH  THE  ARC  VAPOUR.     THE  P.D. 

BETWEEN  THE    ARC  AND  THE   NEGATIVE  CARBON.       THE  DISTURB- 
ANCE  CAUSED  IN  THE  ARC  BY  THE   INSERTION   IN   IT    OF  A    THIRD 

IDLE  CARBON. 

It  has  long  been  known  that  the  principal  fall  of  potential 

in  the  arc  takes  place  between  the  positive  carbon  and  the  arc. 

CV 


years  ago,  Lecher  found  that  if  he  placed  a  third  carbon 
of  l'5mm.  in  an  arc  2'5mm.  in  length,  midway  between  the 
carbons,  the  P.D.  between  the  positive  carbon  and  this  rod 
was  about  35  volts,  while  the  P.D.  between  the  rod  and  the 
negative  carbon  was  about  10  volts.  At  about  the  same 
time  Uppenborn  found  only  about  5  volts  P.D.  between  the 
arc  and  the  negative  carbon.  He  tried  rods  of  copper  or 
platinum  wire,  embedded  in  clay,  in  steatite,  and  in  glass  tubes, 
for  exploring,  but  had  finally  to  abandon  them  all,  in  favour 
of  bare  carbon  rods.  With  these  he  found  that  the  fall 
of  potential  at  the  positive  carbon  varied  between  32'5  and  38 
volts  in  arcs  of  from  6mm.  to  16mm. 

For  some  experiments  made  for  Prof.  Ayrton's  Chicago  Paper 
in  1893,  by  Mr.  Mather,  Mr,  Brousson  and  myself,  a  bare 
carbon  rod  was  placed  close  to  each  main  carbon  in  succession, 
and  thus  the  P.Ds,,  between  the  positive  carbon  and  the  arc 
and  between  the  arc  and  the  negative  carbon,  were  found,  for 
several  currents  and  lengths  of  arc.  The  results  may  be 
summed  up  as  follows  :  — 

(1)  The  curve  connecting  the  fall  of  potential  at  the  positive 
carbon  with  the  current  for  constant  lengths  of  arc  was  very 
much  of  the  same  shape  as  the  similar  curve  for  the  total  P.D. 
across  the  carbons. 

(2)  The  fall  of  potential  at  the  negative  carbon  diminished 
as  the  current  increased,  with  a  constant  length  of  arc. 


208  THE  ELECTRIC  ARC. 

(3)  It  could  not  be  determined  whether  the  fall  of  potential 
at  either  of  the  carbons  depended  on  the  length  of  the  arc  or  not. 

These  results  were  the  first  ever  obtained  showing  any 
definite  connection  between  the  current  and  the  falls  of  poten- 
tial at  each  of  the  carbons,  with  a  constant  length  of  arc  and 
a  varying  current. 

With  the  object  of  obtaining  still  more  definite  information 
as  to  the  laws  connecting  the  value  of  the  current  and  the  length 
of  the  arc  with  the  falls  of  potential  at  the  two  carbons,  I 
have  made  a  series  of  experiments  on  arcs  varying  between 
1mm.  and  7mm,  in  length,  and  using  currents  varying  princi- 
pally between  4  and  14  amperes,  though  a  few  experiments  were 
made  with  larger  currents  with  silent  arcs,  and  some  with 
hissing  arcs. 

The  carbons  used  for  the  whole  series  were,  as  usual,  Apostle 
carbons,  llmm.  in  diameter  for  the  positive  and  9mm.  for  the 
negative.  With  the  greater  part  of  the  experiments  both 
carbons  were  solid,  but  in  order  to  see  what  was  the  effect  of 
the  core  on  the  P.Ds.  in  question,  two  series  of  experiments  were 
made  with  the  positive  carbon  cored  and  negative  solid,  and  two 
with  both  cored,  For  the  first  series  in  each  case  the  current 
was  kept  constant  at  10  amperes,  and  the  length  of  the  arc  varied 
from  1mm  to  7mm.,  and  for  the  second,  the  length  of  the  arc 
was  kept  constant  at  5mm.,  and  the  current  was  varied  between 
the  limits  of  4  and  24  amperes. 

The  exploring  carbons  used  were  mostly  about  1mm.  in  dia- 
meter, a  few  were  thinner,  and  a  few  were  as  thick  as  2mm. 
It  was  found  that  with  the  1mm.  arc  the  most  constant 
results  were  obtained  with  the  thinnest  exploring  carbons, 
while  with  the  longer  arcs  it  was  better  to  use  carbons  of  from 
1mm.  to  l'5mm.  in  diameter;  otherwise,  on  account  of  the 
larger  amount  of  oxygen  with  which  their  hot  parts  came  into 
contact,  they  burnt  away  so  fast  as  to  make  it  difficult  to  obtain 
any  results. 

The  arrangement  was  as  follows  :  The  exploring  carbon 
was  fixed  in  a  metal  holder,  in  which  it  could  be  tilted  either 
up  or  down  but  could  not  be  moved  sideways.  The  holder 
itself  was  moved  by  means  of  two  racks  and  pinions,  one  of 
which  raised  and  lowered  it,  and  the  other  moved  it  horizon- 
tally in  the  direction  of  the  length  of  the  carbon.  The  base  of 


ARRANGEMENT  OF  EXPLORING  CARBON.       209 

the  holder  was  firmly  screwed  to  the  table  to  which  the  lamp 
was  fixed,  in  such  a  position  that  the  vertical  plane  which 
bisected  the  exploring  carbon  longitudinally  also  bisected  the 
arc  carbons  longitudinally,  and  was  parallel  to  the  magnifying 
lens.  Thus  the  image  of  this  carbon  was  thrown  on  to  the 
same  screen  as  that  of  the  arc,  in  such  a  way  that  its  dimen- 
sions and  its  distances  from  the  arc  carbons  and  from  the  arc 
itself  were  all  magnified,  like  the  arc,  ten  times.  Hence  the 
distance  between  the  point  of  the  exploring  carbon  and  any 
point  in  the  arc  or  on  either  of  the  other  carbons  could  be 'deter- 
mined by  simply  measuring  the  distance  between  the  two  corres- 
ponding points  on  the  image,  and  dividing  by  ten.  The  object  of 
tilting  the  carbon  was  to  enable  it  to  be  pushed  right  up  into 
the  crater  or  to  touch  the  extreme  tip  of  the  negative  carbon. 


FIG.  69. — Diagrammatic  Representation  of  Arrangement  of  Main  Carbons 
Exploring  Carbon  and  Voltmeter. 


Fig.  69  shows  diagrammatically  the  arrangement  of  the  three 
carbons  and  the  voltmeter.  V  was  the  voltmeter,  a  high 
resistance  d'Arsonval  galvanometer  with  1,500,000  ohms  in 
circuit,  a,  6,  c,  d  and  e  were  mercury  cups,  E  was  the  exploring 
carbon  and  P  and  N  the  positive  and  negative  carbons  of  the 
arc  respectively,  e  was  permanently  connected  with  E,  a  and  b 
with  the  positive  and  negative  carbons,  and  c  and  d  with  the 
positive  and  negative  poles  of  the  voltmeter,  respectively. 

Now  when  a  and  c  were  connected  by  means  of  one  wire 
bridge  and  e  and  d  by  means  of  another,  the  voltmeter 


210  THE  ELECTRIC  ARC. 

measured  the  P.D.  between  P  and  E,  that  is,  when  E  was  very 
close  to  P,  the  fall  of  potential  at  the  positive  carbon.  When, 
on  the  other  hand,  6  and  d  were  connected,  and  also  c  and  e, 
the  voltmeter  then  measured  the  P.D.  between  N  and  E,  or, 
when  E  was  very  close  to  N,  it  measured  the  fall  of  potential 
at  the  negative  carbon. 

The  following  was  the  method  of  experimenting : 
When  the  arc  was  normal  with  a  given  current  and  length 
(see  definition  of  a  normal  arc,  p.  104),  the  idle  carbon, 
properly  tilted,  was  brought  into  it  with  its  point  in  the  centre, 
midway  between  the  two  carbons.  In  a  few  seconds  this  third 
carbon  grew  beautifully  pointed  and  its  tip  became  white 
hot.  It  was  then  raised  or  lowered  till  the  tip  touched  the 
crater  of  the  positive,  or  the  white  hot  spot  on  the  negative — 
the  "  white  spot,"  as  I  shall  call  it — according  to  the  P.D.  it 
was  desired  to  measure.  The  slow  motion  of  the  voltmeter 
needle,  as  the  idle  carbon  was  moved  through  the  arc,  was 
very  different  from  the  rush  it  made  when  the  two  carbons 
touched ;  hence,  the  last  reading  before  they  touched  was 
very  easy  to  observe,  after  a  little  experience,  and  this  was 
obviously  the  reading  that  gave  most  nearly  the  true  fall 
of  potential  at  the  main  carbon.  The  employment  of  a  bare 
carbon  for  such  measurements  has  its  disadvantages,  but 
these  are  much  less  when  used  as  described  above  than  when 
the  rod  is  merely  held  in  a  stationary  position  in  the  arc,  as 
has  always  hitherto  been  done.  Indeed,  the  results  of  two 
complete  series  of  experiments,  conducted  on  the  old  stationary 
method,  had  to  be  abandoned,  because  they  were  so  vague  that 
no  conclusions  could  possibly  be  drawn  from  them.  But  by 
making  the  rod  actually  touch  the  hottest  part  of  the  main 
carbon,  the  fall  of  potential  at  a  perfectly  definite  point  was 
always  measured,  and  this  led  to  very  accurate  and  constant 
readings. 

One  great  difficulty  in  this  mode  of  measurement  is  caused 
by  the  third  carbon  repelling  the  arc  when  it  approaches  it. 
This  repulsion  is  greater  the  longer  the  arc  and  the  smaller  the 
current,  so  that  with  long  arcs  and  small  currents  it  is  difficult 
to  get  the  idle  carbon  into  the  arc  at  all.  The  arc  slips  away  from 
the  carbon  exactly  as  if  the  one  were  an  air  ball  suspended  by 
its  two  ends  and  the  other  were  trying  to  penetrate  it.  Under 


EFFECTS  DUE  TO  TRIED  CARBON.  211 

certain  circumstances,  not  yet  very  well  defined,  the  carbon 
appears  to  attract  the  arc  when  once  it  has  been  made  to  dip 
well  into  it.  This  subject  of  the  repulsion  and  attraction  of  the 
arc  by  the  third  carbon  would  well  repay  further  investigation. 

The  third  carbon  disturbs  the  arc  in  other  ways  as  well  as 
by  repelling  it.  If  left  in  long  enough  near  either  carbon, 
it  grows  by  receiving  carbon  from  it,  especially  when  left  close 
to  the  positive  pole.  It  also  cools  the  arc  at  first,  and  it  alwavs 
disturbs  the  distribution  of  potential  in  it.  The  first  difficulty 
is  overcome  by  allowing  the  third  carbon  to  remain  for  only  a 
short  time  close  to  either  carbon  ;  the  second  by  keeping  it  for 
a  little  while  in  the  centre  of  the  arc  before  bringing  it  up  to 
the  main  carbon  to  take  a  reading.  The  third  has  to  be 
allowed  for  in  our  interpretation  of  the  results  of  the 
experiments. 

It  has  been  mentioned  that  the  third  carbon  always 
becomes  beautifully  pointed  when  placed  in  the  arc.  This  is 
the  case  when  its  diameter  is  small  compared  with  those  of  the 
main  carbons,  but  I  found  that  when  a  flat  rod  was  inserted  so 
as  to  screen  the  hot  parts  of  the  two  carbons  from  one  another, 
two  arcs  formed — one  between  the  positive  carbon  and  the  rod, 
and  one  between  the  rod  and  the  negative  carbon ;  and  in  that 
case  the  rod  became  cratered  on  the  side  opposite  to  the  nega- 
tive carbon  and  a  small  rough  excresence  formed  on  the  side 
opposite  to  the  positive  carbon.  It  was  not  possible  to  detect 
the  presence  of  the  two  arcs  from  the  image,  which  showed, 
apparently,  only  one  big  arc,  but  the  voltmeter  indicated  it  at 
once,  for,  as  soon  as  the  second  arc  was  formed,  the  voltmeter 
deflection  became  nearly  doubled. 

In  order  to  eliminate  any  error  that  deficiences  in  the 
hardness  and  texture  of  the  carbons  might  introduce,  even 
though  they  were  all  of  the  same  make,  none  were  employed 
except  those  of  which  the  total  P.D.  across  the  carbons  with 
the  normal  arc  used  was  within  a  half  a  volt  of  that  given  by 
equation  (3)  (p.  184),  for  the  same  length  of  arc  and  current. 

Lecher,  using  a  bare  carbon  rod  as  I  have  done,  but  keeping 
it  stationary  in  the  arc  instead  of  making  it  touch  the  main 
carbon,  found  the  positive  carbon  P.D.  to  be  about  35  volts. 
Uppenborn,  by  the  same  means,  found  that  it  varied  between 
32 -5  and  38  volts  for  arcs  of  from  6mm.  to  16mm.,  while  Luggin 

r2 


212  THE  ELECTRIC  ABC. 

obtained  337±0'46  volts  for  the  value  with  a  current  of  15-5 
amperes,  and  could  observe  no  change  when  he  changed 
the  length  of  the  arc.  All  these  results  agree  very  well  with 
one  another,  as  far  as  they  go ;  but,  in  order  to  find  out  what 
effect  changes  in  the  current  and  the  length  of  the  arc  had 
on  the  P.Ds.,  it  was  necessary  to  make  a  complete  series  of 
experiments,  using  many  different  currents  and  lengths  of  arc, 
and  finding  the  value  of  the  P. D.  between  each  carbon  and  the  arc 
separately  with  each  current  and  length  of  arc.  Such  a  series 
of  experiments  I  have  made,  and,  as  a  check  upon  the  results, 
I  also  observed  the  P.D.  between  each  carbon  and  the  arc  plus 
the  P.D.,  through  the  arc  vapour  itself,  so  that,  subtracting 
these  P.Ds.  from  the  total  P.D.  across  the  main  carbons,  I 
might  get  indirect  measurements  of  the  P.D.  between  each 
carbon  and  the  arc,  as  well  as  the  direct  measurements. 
Thus  four  sets  of  cases  were  observed  : 

(1)  The  P.D,  between  the  positive  carbon  and  the  third 
carbon,  just  before  the  point  of  the  latter  touched  the  crater. 

(2)  The  P.D.  between  the  third  carbon  and  the  negative 
carbon,  just  before  the  point  of  the  former  touched  the  white 
spot. 

(3)  The  P.D.  between  the  positive   carbon  and   the    third 
carbon,  just  before  the  point  of  the  latter  touched  the  white 
spot. 

(4)  The  P.D.  between  the  third  carbon  and  the  negative 
carbon,   just    before   the   point   of    the   former   touched   the 
crater. 

The  first  and  second  P.Ds.  we  may  call,  for  convenience 
sake,  the  positive  and  negative  carbon  P.Ds.,  respectively ; 
the  third  and  fourth  are  those  same  P.Ds.  with  the  P.D. 
through  the  arc  vapour  itself  added.  This  last  P.D.  we  may 
call  the  vapour  P.D. 

The  whole  four  cases  are  represented  diagrammatically  in 
Fig.  70 — (1)  shows  how  the  positive  carbon  P.D.  was  measured, 
(2)  the  negative  carbon  P.D.,  (3)  the  positive  carbon  P.D.  plus 
the  vapour  P.D.,  (4)  the  vapour  P.D.  plus  the  negative  carbon 
P.D.  In  the  first  two  cases  the  P.D.  rushed  down  to  zero  when 
the  carbons  touched  one  another,  in  the  last  two  it  rushed  up 
till  it  reached  the  value  of  the  total  P.D.  across  the  main 
carbona.  In  each  case  the  motion  of  the  voltmeter  needle, 


CAEBON  AND  VAPOUR  P.Ds. 


213 


when  the  exploring  carbon  touched  the  main  carbon,  was  very 
much  quicker  than  it  had  been  before  they  touched,  so  that 
the  last  deflection,  before  they  touched  could  be  read  with  a 
fair  amount  of  ease.  Each  experiment  was  repeated  at  least 
six  times,  and  if  the  readings  of  any  particular  P.D.  differed 
much  from  one  another,  twelve  or  even  more  measurements 
of  it  were  made.  Tables  XXVIL,  XXVIIL,  XXIX.  and  XXX. 
contain  the  means  of  the  results  of  the  four  series  of  experi- 
ments with  solid  carbons  and  silent  arcs. 


(2) 


FIG.  70. — Diagrammatic  Representation  of  Arrangement  of  Main  Carbons 
and  Exploring  Carbon.  (1)  Positive  Carbon  P.D.,  (2)  Negative  Carbon 
P.D.,  (3)  Positive  Carbon  P.D.  +  Vapour  P.D.,  (4)  Vapour  P.D.  +  Nega- 
tive Carbon  P.D. 

Table  XXVIL  gives  the  positive  carbon  P.D.,  as  nearly  as  it 
can  be  measured,  by  means  of  a  bare  carbon  placed  in  the  arc. 
All  such  measurements  are  subject  to  the  possibility  that  the 
idle  carbon  may  not  take  up  the  potential  of  the  part  of  the  arc 
in  which  it  is  placed,  that  is,  there  may  be  a  contact  P.D.  between 
this  solid  carbon  and  the  vaporous  stuff  of  which  the  arc 
consists.  But,  even  if  it  exists,  this  P.D.  is  probably  very  small 
compared  with  those  under  consideration,  and  need  not,  therefore, 
be  taken  into  account. 


214 


THE  ELECTRIC  ARC. 


Table  XXVII. — P.D.  between  Positive  Carbon  and  Third  Carbon 

with  Point  of  Latter  close  to  Crater  of  Former. 
All  carbons  solid.      Positive,  llmm.  ;  negative,  9mm.  ;   third 
carbon,  0'5mm.  to  2mm. 


Current 
iii 

P.D.  in  Volts. 

Amperes. 

1  =  1. 

1=2. 

J=3. 

J=4. 

1=5. 

1  =  6. 

1  =  1. 

4 

34-3 

370 

38-6 

38-5 

36-7 

39-7 

39-0 

5 

33-6 

330 

342 

34-5 

355 

36-9 

37-7 

6 

34-95 

35-2 

31-0 

33-9 

35-55 

36-6 

36-1 

7 

33-25 

33-8 

33-3 

331 

350 

361 

36-9 

8 

32-7 

32-75 

32-6 

33-3 

349 

33-8 

35-2 

9 

33-3 

33-9 

34-85 

35-1 

35-4 

36-1 

34-5 

10 

32-6 

32-4 

31-5 

33-75 

33-5 

32-7 

34-7 

12 

31-9 

32-8 

32-2 

32-7 

33-8 

33-4 

34-4 

14 

31-4 

31-8 

32-5 

31-8 

34-8 

36-2 

16 

... 

... 

32-5 

32-7 

33-1 

33-0 

20 

- 

... 

... 

... 

34-2 

33-6 

Table  XXVIL  shows  that  the  positive  carbon  P.D.  is  not  a 
constant,  but  that,  like  the  total  P.D.  between  the  main  carbons 
of  the  arc,  it  diminishes  as  the  current  increases,  and  increases 
as  the  length  of  the  arc -increases.  But  the  degree  of  diminu- 
tion and  of  increase  is  very  different  in  the  two  cases,  for  while 
the  total  P.D.  between  the  carbons  ranges  from  42 '3  volts  for  a 
1mm.  12  ampere  arc  to  74'4  volts  for  a  7mm.  4  ampere  arc 
(Fig.  38,  p.  120),  the  positive  carbon  P.D.  given  in 
Table  XXVIL  varies  only  from  31-9  volts  to  39  volts  for 
the  same  range  of  current  and  length  of  arc.  That  is,  the 
total  P.D.  between  the  carbons  has  a  range  of  about  32 
volts,  while  the  positive  carbon  P.D.  has  a  range  of  only 
about  7  volts  for  the  same  variation  of  length  and  current. 
Hence,  at  any  rate,  when  measured  with  a  bare  carbon  rod 
(and  no  better  means  of  measurement  has  yet  been  devised), 
the  fall  of  potential  at  the  positive  carbon  is  not  a  constant,  but 
varies  both  with  the  length  of  the  arc  and  the  current,  in  the  same 
way,  but  to  afar  less  extent  than  the  total  P.D.  between  the  carbons. 

This  will  be  seen  even  more  clearly  from  the  curves  in 
Figs.  71  and  72,  which  were  plotted  from  the  numbers  in 
Table  XXVII.  In  Fig.  71  the  curves  show  the  connection 
between  the  positive  carbon  P.D.  and  the  current,  for  constant 
lengths  of  arc,  and  in  Fig.  72  the  connection  between 
the  same  P.D.  and  the  length  of  the  arc,  for  various 


POSITIVE  CARBON  P.D. 


215 


constant  currents.  Had  these  lines  all  been  drawn  from 
the  same  zero  of  P.D.,  they  would  have  been  so  close 
together  that  it  would  have  been  difficult  to  distinguish  one 
line  from  another.  The  zero  of  P.D.  has,  therefore,  been  raised 
5  volts  for  each  line,  as  the  numbers  on  either  side  of  the 
figures  show.  Thus  the  lines  are  all  drawn  to  the  same  scale, 
but  each  has  a  different  point  for  its  zero  of  P.D. 


4  0  8  10  1*  14 

Current  in  Amperes. 

FIG.  71. — Positive  Carbon  P.D.  and  Current  for  Various  Constant 

Lengths  of  Arc. 

Solid  Carbons :  Positive,  llmm.  ;  negative,  9mm.  ;  third  carbon,  O'Snitn. 

to  2mm. 

The  curves  in  Fig.  71  are  evidently  not  unlike  those  in 
Fig.  38  (p.  120),  for  the  total  P.D.  across  the  main  carbons 
•with  constant  lengths  of  arc,  but  they  are  flatter.  That  is,  as 
was  seen  from  the  Table,  for  a  given  range  of  current  the 
range  of  the  P.D.  across  the  main  carbons  is  much  greater 
than  the  range  of  the  P.D.  between  the  positive  carbon  and 


216 


THE  ELECTRIC  ARC. 


the  arc.  Similarly,  comparing  the  continuous  lines  in  Fig.  72 
with  those  in  Fig.  44  (p.  136),  we  find  that  both  are  straight  lines 
converging  towards  one  another  on  the  left  hand  side,  but 


012345 
Length  of  Arc  in  Millimetres. 
FIG.  72.— Positive  Carbon  P.D.  and  Length  of  Arc  for  Various 

Constant  Currents. 

Solid  carbons  :   Positive,  llmm. ;  negative,  9mm.  ;  third  carbon,  0  5mm. 

to  2mm. 

that  the  lines  in  Fig.  44  are  much  the  steeper,  showing 
that  the  range  of  P.D.  for  any  given  range  of  length  of  arc  is 
considerably  greater,  with  the  same  constant  current,  for  the 


NEGATIVE  CARBON  P.D. 


217 


total  P.D.  across  the  carbons  than  for  the  positive  carbon  P.D. 
Had  the  lines  in  Fig.  72  all  been  drawn  to  the  same  zero,  it 
would  be  found  that  they,  as  well  as  those  in  Fig.  44,  all  met 
at  a  point  to  the  left  of  the  axis  of  P.D.,  showing  that  there 
is  no  real  length  of  arc  for  which  the  positive  carbon  P.D.  is 
the  same  for  all  currents.  The  meaning  of  the  dotted  lines  in 
Fig,  72  is  explained  later,  p.  223. 

Turning  now  to  the  negative  carbon  P.D.,  this  has  been  stated 
by  some  observers  to  change  its  direction  when  the  arc  hissed, 
i.e.,  instead  of  the  arc  near  the  negative  carbon  being  at  a 
higher  potential  than  the  negative  carbon  itself,  these  observers 
thought  that  with  hissing  arcs  the  negative  carbon  was  at 
a  higher  potential  than  the  parts  of  the  arc  nearest  to  it.  I 
have  never  found  this  to  be  the  case,  either  with  silent  or 
hissing  arcs  ;  whether  cored  or  solid  carbons  were  used.  The 
fall  of  potential  at  the  positive  pole  is  always  from  carbon  to 
arc,  and  at  the  negative  pole  from  arc  to  carbon,  so  that  the 
potential  falls  continuously  from  the  positive  carbon  through 
the  arc  to  the  negative  carbon.  Other  observers  have  denied 
the  existence  of  a  fall  of  potential  between  the  arc  and  the 
negative  carbon,  but  these  experiments  conclusively  prove  that 
they  are  wrong,  and  shows  that  with  the  carbons  I  used  this 
fall  of  potential  cannot  be  less  than  7'6  volts. 

Table  XXVIII. — P.D.  between  Third  Carbon  and  Negative  Car- 
bon with  Point  of  Former  close  to  White  Hot  Spot  on  Latter. 
All  carbons  solid.     Positive,  llmm. ;  negative,  9mm.;  third 
carbon,  0'5mm.  to  2mm. 


Current 

P.D.  in  Volts. 

Amperes. 

1  =  1.    \    1=2. 

1=3. 

Z=4. 

1  =  5. 

1  =  6. 

Z=7. 

4 

12-9 

11-5 

12-9 

12-2 

10-4 

10-6 

10-3 

5 

iO-1 

10-1 

11-2 

104     I     10-8 

10-7 

9-9 

6 

8'6 

10-3 

9-6 

9-4 

9-7 

9-2 

9-3 

7 

8-8 

9-8 

9-6 

9-4 

9-4 

9-5 

9-6 

8 

8-2 

8-8 

10-9 

9-3 

10-0 

9-3 

8-9 

9 

7-8 

8-8           8-9 

91 

9-6 

9-0 

9-0 

10 

8-5 

8-5           9-0 

8-9     i       9-2 

9-2 

9-2 

12 

8-5 

8-4           9'2 

9-3     !       9-6 

8-8 

8-7 

14 

9-7 

9-2 

9-3 

9-2 

9-0 

8-9 

16 

... 

9-3 

9-2 

91 

9-1 

20 

... 

... 

... 

... 

... 

9-6 

9-2 

218 


THE  ELECTRIC  AEG. 


Table  XXVIII.  gives  the  values  of  the  negative  carbon  P.D. 
for  the  same  currents  and  lengths  of  arc  as  those  for  which 
the  P.Ds.  between  the  positive  carbon  and  the  arc  were 
given  in  Table  XXVII. 

It  is  quite  plain,  from  these  numbers,  that  the  negative 
carbon  P.D.  diminishes  as  the  current  increases,  following,  in 
this  respect,  the  same  law  as  the  total  P.D.  across  the  carbons, 


024  6  8  10  12 

Current  in  Amperes. 

FIG.  73. — Negative   Carbon   P.D.  and    Current  for  Various  Constant 

Lengths  of  Arc. 

Solid  Carbons  :  Positive,  llmm. ;  negative,  9mm, ;  third  carbon, 
O'Smm.  to  2mm. 

and  the  positive  carbon  P.D.  But  how  it  is  affected  by  a 
change  in  the  length  of  the  arc  it  is  impossible  to  see  without 
reference  to  the  curves  plotted  from  the  numbers.  These  are 
given  in  Figs.  73  and  74,  in  which,  like  those  in  Figs.  71 
and  72,  each  curve  is  drawn  from  a  separate  zero  of  P.D.  in 
order  to  prevent  overcrowding. 


NEGATIVE  CARBON  P.D. 


219> 


In  Fig.  73  the  curves  connect  negative  carbon  P.D.  with 
current  for  constant  lengths  of  arc.  They  are  like  the  similar 
curves  in  Figs.  71  and  38,  but  are  much  flatter  than  either, 
showing  that,  for  a  given  length  of  arc,  the  negative  carbon 
P.D.  varies  considerably  less  than  The  total  P.D.  across  the 
carbons,  or  even  than  the  positive  carbon  P.D.,  for  the  same 
variation  of  current. 


01  23456 

Length  of  Arc  in  Millimetres. 
FIG.  74.— Negative  Carbon  P.D.  and  Length  of  Arc  for  Various  Constant 

Currents. 

Solid  Carbons  :  Positive,  llmm.  ;  negative,  9mm.  ;  third  carbon, 
0'5mm.  to  2mm. 

The  lines  in  Fig.  74,  which  connect  the  negative  carbon 
P.D.  with  the  length  of  the  arc  for  constant  currents,  show 


220 


THE  ELECTEIC  ARC. 


that  that  P.D.  is  not  affected  at  all  by  a  change  in  the  length 
of  the  arc,  for,  except  the  line  for  4  amperes,  they  are  all 
practically  horizontal  straight  lines.  Thus,  when  measured  by 
means  of  a  bare  carbon  rod,  the  P.D.  between  the  arc  and  the 
negative  carbon  varies  with  the  current,  but  not  with  the  length 
of  the  arc. 

With  the  help  of  Figs.  75,  76,  and  77,  it  will  be  easy  to 
construct  equations  similar  to  equation  (3)  (p.  184),  for 
connecting  each  of  the  carbon  P.Ds.  with  the  current  and  the 
length  of  the  arc.  The  lines  in  these  figures  are  all  power 
lines,  and  the  power  is  measured  in  each  case  by  multiplying 


500 


1  2  3  4  5  6  7 

Length  of  Arc  in  Millimetres. 
FIG.  75.— Positive  Carbon  Power  and  Length  of  Arc  for  Various  Constant 

Currents. 

Solid  Carbons  :  Positive,  llmm.  ;  negative,  9mm.  ;  third  carbon, 
O'Srnin.  to  2mm. 

the  carbon  P.D.  by  the  current.  For  convenience  sake  we 
shall  call  the  positive  carbon  P.D.,  multiplied  by  the  current, 
the  positive  carbon  power,  and  the  negative  carbon  P.D., 
multiplied  by  the  current,  the  negative  carbon  power. 

Fig,  75  shows  the  connection  between  the  positive  carbon 
power  and  the  length  of  the  arc  for  constant  currents.  The 
lines  are  all  straight,  as  are  the  similar  ones  for  the  total 
power  consumed  in  the  arc  (Fig.  62,  p.  180),  but  whereas  the 


POSITIVE  CARBON  POWER. 


221 


total  power  lines  converge  towards  one  another,  the  positive 
carbon  power  lines  are  all  parallel. 

Similarly,  the  lines  in  Fig.  76,  which  show  the  connection 
between  the  positive  carbon  power  and  the  current  for 
constant  lengths  of  arc,  are  also  parallel  straight  lines,  while 


02  4  6  8  10 

Current  in  Amperes 

>  76. — Positive  Carbon  Power  and  Current  for  Various   Constant 

Lengths  of  Arc. 

Solid  Carbons :  Positive,  llmm.  ;  negative,  9mm. ;  third  carbon, 
0'5mm.  to  2mm. 


222  THE  ELECTEIG  AEC. 

the  similar  lines  for  the  total  power  consumed  in  the  arc, 
although  straight,  are  not  parallel,  but  all  meet  at  a  point 
(Fig.  63,  p.  182). 

To  find  the  equation  connecting  the  positive  carbon  P.D. 
with  the  current  and  the  length  of  the  arc,  we  have  the 
equation  to  any  one  of  the  lines  in  Fig.  75 

W-W1_Wy-W1 

l-l      ~~   7-1     ' 

where  W  is  the  positive  carbon  power  in  watts  for  length  of 
arc  I  mm., 

Wi  is  the  positive  carbon  power  in  watts  for  length  of 

arc  1mm., 
\V7  is  the  positive  carbon  power  in  watts  for  length  of 

arc  7mm. 

From  the  lines  in  Fig.  76,  which  show  the  connection  between 
the  positive  carbon  power  and  the  current  for  constant  lengths 
of  arc,  we  can  find  Wj  and  W*, 

Wl  -  137-2  _  3874  -137-2 
12-4       ' 


7  =  31-28A+30-7. 
Hence,  in  the  equation  connecting  W  and  I,  we  have 

W-31-28A-12-1  =  31  -28A  +  30-7  -(31-28A+  12-1) 
l-l  6 

18-6 

'~ir 

=  3-1 

.'.  W  =  31-2SA  +  12-l+31/-3-l, 
or  W  =  31  28A  +  9  +  3-1Z. 

Dividing  all  through  by  A,  we  have 

>  (6) 

for  the  equation  connecting  the  positive  carbon  P.D.  with  the 
current  and  the  length  of  the  arc. 

This  equation,  like  the  similar  one  for  the  total  P.D.  across 
the  carbons  (p.  184),  is  the  equation  to  a  series  of  rectangular 


POSITIVE  CARBON  P.Ds. 


223 


hyperbolas,  but,  whereas  with  the  total  P.D.  the  hyperbolas 
have  only  one  asymptote  in  common,  with  the  positive 
carbon  P.D.  they  have  both  asymptotes  in  common;  one,  the 
axis  of  P.D.,  and  the  other,  a  line  parallel  to  the  axis  of 
current,  at  a  distance  from  it  equal  to  31-28  times  the  distance 
taken  to  represent  one  volt.  Table  XXIX.  gives  the  positive 
carbon  P.Ds.  calculated  from  equation  (6)  for  all  the  currents 
and  lengths  of  arc  for  which  values  were  obtained  by  experiment. 

Table  XXIX. — Positive  Carbon  P.Ds.  calculated  from  Equa- 
tion (6). 

Solid   carbons.      Positive,    llmm. ;    negative,    9mm. ;     third 
carbon,  0'5mm.  to  2mm. 


Current  in 

P.D.  in  Volts. 

Amperes. 

1  =  1. 

1  =  2. 

Z=3. 

Z=4. 

1=5. 

1  =  6. 

1  =  1. 

4 

34-3 

35-1 

35-9 

36-6 

37-4 

38-2 

39-0 

5 

33-7 

Z4-3 

34-9 

35-6 

36-2 

36-8 

37-4 

6 

33-3 

33-8 

34-3 

34-85 

35-4 

35-9 

36-4 

7 

33-0 

33-45 

33-9 

34-3 

34-8 

35-2 

35-7 

8 

32-8 

33-2 

33-6 

34-0 

34-3 

34-7 

35-1 

9 

32-6 

33-0 

33-3 

33-7 

34-0 

34-35 

34-7 

10 

32-5 

32-8 

33-1 

33-4 

33-7 

34-0 

34-35 

12 

32-3 

32-55 

32-8 

33-1 

33-3 

336 

33-8 

14 

32-4 

32-6 

32-8 

33-0 

33-25 

33-5 

16 

32-6 

32-8 

33-0 

33-2 

20 

... 

... 

32-7 

32-8 

A  comparison  of  the  two  Tables  XXVII.  and  XXIX.  shows 
that  of  the  68  calculated  P.Ds.,  47  differ  from  the  observed 
P.Ds.  by  one  volt  or  less,  18  more  by  less  than  two  volts, 
and  only  three  differ  by  more  than  two  volts.  Considering 
the  many  possibilities  of  error  in  the  observation  of  these 
P.Ds.,  the  equation  must  be  allowed  to  fit  the  experi- 
mental results  with  great  accuracy.  To  show  exactly  what 
is  the  degree  of  accuracy,  the  dotted  lines  in  Fig.  72 
have  been  drawn.  These  lines  are  the  ones  obtained  from 
equation  (6),  while  the  complete  lines  are  drawn  as  nearly 
as  possible  through  the  average  positions  of  the  observed 
points. 

To  obtain  the  equation  connecting  the  negative  carbon  P.D. 
with  the  current  and  the  length  of  the  arc,  the  equation  to  the 


224 


THE  ELECTRIC  AEC. 


line  in  Fig.  77  only  is  required.  The  points  for  this  line  were 
found  by  taking  the  average  negative  carbon  P.D.  for  each 
current  from  Table  XXVIIL,  and  multiplying  it  by  the  current. 


£        2CO 

0. 

1 

S°» 

JL 

—  —  1 

g 

^ 

>—*--' 

,  o  \ 

>  —  " 

5             0 

12 


14 


k§>  2  4  6  8  10 

Current  in  Amperes. 

FIG.  77. — Negative  Carbon  Power  and  Current  for  All  Lengths  of  Arc. 

Solid  Carbons  :    Positive  llmm.  ;  negative  9mm. ;  third  carbon, 

0'5mm.  to  2mm. 

This  was  done  because  it  was  found  from  the  curves  (p.  219)  that 
with  a  given  current  the  negative  carbon  P.D.  was  the  same 
for  all  lengths  of  arc. 

The  equation  to  the  line  in  Fig.  77  is 
W-44_12Q-44 
A-4  =        10 

=  7-6. 

Hence  W  =  7'6A  +  13-6. 

And,  dividing  all  through  by  A,  we  have 

T-»*¥ <•> 

for  the  equation  connecting  the  negative  carbon  P.D.  with  the 
current  and  the  length  of  the  arc.  This  is  the  equation  to  a 
single  rectangular  hyperbola  of  which  the  asymptotes  are  the 
axis  of  P.D.,  and  a  line  parallel  to  the  axis  of  current,  at  a 
distance  from  it  7*6  times  the  distance  which  represents  one  volt. 

Table  XXX.  gives  the  negative  carbon  P.Ds.  calculated  from 
equation  (7)  for  all  the  currents  for  which  such  P.Ds.  were 
obtained  by  experiment. 

Comparing  these  values  with  those  in  Table  XXVIII.,  it  will 
be  found  that,  of  the  68  observed  values,  42  differ  from  the 
calculated  values  by  half  a  volt  and  under,  16  more  by  less 
than  one  volt,  and  9  by  between  one  and  two  volts.  Thus 
equation  (7)  may  fairly  be  taken  to  represent  the  connection 
between  the  negative  carbon  P.D.,  the  current,  and  the  length 
of  the  arc. 


NEGATIVE  CARBON  P.Ds. 


225 


Table   XXX. — Negative  Carbon   P.Ds.  calculated  from  Equa- 
tion (7). 

Solid   carbons.      Positive,    llmm. ;    negative,    9mm. ;    third 
carbon,  O'Smm.  to  2mm. 


Current  in 
Amperes. 

P.D.   in  Volts. 

Current   in 
Amperes. 

P.D.  in  Volts. 

4 
5 
6 
7 
8 
9 

11-0 
10-3 
9-9 
9'5 
9-3 
91 

10 
12 
14 
16 
20 

9-0 
87 
8-6 
8-45 
8-3 

From  equations  (6)  and  (7)  we  can  find  the  equation  for 
the  positive  carbon  P.D.  plus  the  negative  carbon  P.D. ;  i.e., 
the  whole  fall  of  potential  from  carbon  to  carbon  minus  the 
fall  of  potential  through  the  arc  itself.  It  is 


V-  38-88  + 


(8) 


Now  equation  (3)   for   the  total  P.D.    between    the    main 
carbons,  which  includes,  of  course,  the  drop  of  P.D.  in  the  arc 

itself,  is 


V-  38-88  +  2-07 


(3) 


The  coincidence  between  the  first  terms  of  equations  (8)  and 
(3)  shows  that  this  constant  quantity  belongs,  not  to  the 
positive  carbon  alone,  as  has  hitherto  been  supposed,  but  to 
both  the  positive  and  negative  carbons  in  the  proportion  of 
about  four-fifths  to  the  former  and  one-fifth  to  the  latter. 

Hence,  if,  as  many  investigators  imagine,  this  constant  term 
involves  the  existence  of  a  constant  back  E.M.F.  in  the  arc, 
this  back  E.M.F.  must  be  considered  to  reside,  not  at  the 
positive  carbon  alone,  as  has  hitherto  been  taken  for  granted, 
but  at  both  carbons  ;  and  this  fact  will  necessitate  a  considerable 
modification  in  any  theory  of  the  arc  yet  enunciated  that 
involves  the  existence  of  a  constant  back  E.M.F. 

Table  XXXI.  gives  the  sum  of  the  observed  values  of  the  two 
carbon  P.Ds.,  taken  from  Tables  XXVII.  and  XXVIII. 
Table  XXXII.  shows  the  corresponding  values  calculated  from 


226 


THE  ELECTRIC  ARC. 


equation  (8).  From  a  comparison  of  these  two  tables  it  will 
be  seen  that,  of  the  62  calculated  values,  39  differ  from  the 
observed  values  by  one  volt  and  under,  18  by  two  volts  and 
under,  and  5  by  more  than  two  volts.  Although  the  calculated 
values  for  the  sum  of  the  two  carbon  P.Ds.  appear  to  agree  less 
perfectly  with  the  observed  values  than  those  for  each  carbon 
separately,  yet  it  will  be  found  that  the  curves  in  Fig.  78, 
which  have  been  taken  from  equation  (8),  go  almost  exactly 


8  10  12  14 

Current  in  Atnperes. 

FIG.  78.— Positive  Carbon  P.D.  plus  Negative  Carbon  P.D.,  and  Current. 

for  Various  Constant  Lengths  of  Arc. 

Solid  Carbons  :  Positive,  llmm.  ;  negative,  9mm.  ;  third  carbon, 
0'5mm.  to  2mm. 

through  the  average  position  of  the  observed  points,  which  are 
the  ones  given  in  the  figure ;  showing,  of  course,  that  equation 
(8)  does  really  represent  very  accurately  the  connection 
between  the  sum  of  the  two  carbon  P.Ds.,  the  current,  and  the 
length  of  the  arc. 


SUM  OF  CABBON  P.Ds. 


227 


Table  XXXI. — Sum  of  the  observed  Values  of  the  Two  Carbon 

P.Ds.  taken  from  Tables  XXVII.  and  XXVIII. 
Solid  carbons.     Positive,  llmm. ;   negative,  9mm.  ;  third  car- 
bon, 0'5nim.  to  2mm. 

P.D.  in  Volts. 


•Current  in 
Amperes. 

1=1. 

4 

47-2 

5       i     43-7 

6 

43-55 

7 

42-05 

8 

40-9 

9 

41-1 

10 

41-1 

12 

40-4 

14 

... 

16 

20 

... 

1=2. 

Z=3. 

Z=4. 

1  =  5. 

1  =  6. 

1-7. 

48-5 

51-5 

50-7 

47-1 

50-3 

49-3 

43-1 

45-4 

44-9 

46-3 

47-6 

47-6 

45-5 

40-6 

43-3 

45-25 

45-8 

45-4 

43-6 

42-9 

42-5 

44-4 

45-6 

46-5 

41-55 

43-5 

42-6 

44-9 

43-1     !     44-1 

42-7 

43-75 

44-2 

45-0 

45-1     !    43-5 

40-9 

40-5 

42-65  i     42-7 

41-9     |     43-9 

41-2 

41-4 

42-0 

43-4 

42-2     '     43-1 

41-1 

41-0 

41-8 

41-0 

43-8 

45-1 

... 

41-8 

41-9 

42-2 

42-1 

... 

43-8 

42-8 

Table  XXXII. —  Values  of  the  Sum  of  the  Tivo  Carbon  P.Ds.  cal- 
culated from  Equation  (8). 

Solid  carbons.     Positive,  llmm.  ;  negative,  9mm,.  ;  third  car- 
bon, 0'5mm.  to  2mm. 


Current  in 
Amperes. 


P.D.  in  Volts. 


4 
5 
6 
7 
8 
9 

10 
12 
14 
16 
20 


1=1. 

1=2. 

J=3. 

Z=4. 

1=5. 

1  =  6. 

1  =  7. 

45-3 

46-1 

46-85 

47-6 

48-4 

49-2 

49-95 

44-0 

44-6 

45-3 

45-9 

46-5 

47-1 

47-7 

43-2 

43-7 

44-2 

44-7 

45-2 

45-75 

46-3 

42-55 

43-0 

43-4 

43-9 

44-3 

44.8 

45-2 

42-1 

42-5 

42-9 

43-3 

43-6 

44-0 

44-4 

41-7 

42-1 

42-4 

42-8 

43-1 

43-5 

43-8 

41-45 

41-8 

42-1 

42-4 

42-7 

43-0 

43-3 

41-0 

41-3 

41-5 

41-8 

42-05 

42-3 

42-6 

... 

40-9 

41-15 

41-4 

41-6 

41-8 

42-0 

... 

411 

41-3 

41-5 

41-7 

... 

... 

... 

... 

40-9 

411 

So  far  it  has  been  taken  for  granted  that  the  P.D.  measured 
by  the  voltmeter,  between  the  main  carbon  and  the  bare  idle 
carbon  dipping  into  the  arc,  was  the  actual  fall  of  potential 
between  the  main  carbon  and  the  arc.  That  this  is  not 
absolutely  the  case  is  quite  certain,  for  the  bare  carbon 
must  bring  all  the  parts  of  the  arc  that  it  touches  to  practi- 
cally the  same  potential.  And  this  potential  will  be  greater 

Q2 


228  THE  ELECTE1G  AEG. 

than  the  least  and  less  than  the  greatest  of  the  potentials 
that  existed  in  the  arc  before  the  insertion  of  the  exploring 
carbon. 

Thus  it  is  quite  possible  that  the  variable  part  of  the  fall  of 
potential  at  each  of  the  carbons,  given  by  equations  (7)  and  (8), 
may  be  mainly  produced  by  the  exploring  carbon  being  in 
communication  with  the  arc,  not  only  at  its  tip,  but  also  along 
a  part  of  its  length.  For,  whether  the  fall  of  potential  at  the 
carbon  itself  be  a  constant  or  not,  it  is  quite  certain  that  the 
potentials  of  the  other  points  at  which  the  arc  touches  the 
exploring  carbon  vary  both  with  the  current  that  was  flowing 
and  with  the  length  of  the  arc,  before  that  carbon  was  inserted. 
Hence,  at  least  a  portion  of  the  variation  in  the  values  given  by 
equations  (6)  and  (7)  must  have  been  created  by  the  use  of  a 
bare  carbon  in  the  arc. 

It  is  possible  to  show,  however,  at  least  indirectly,  that  the 
part  of  the  variation  of  P.D.  that  depends  upon  the  current 
alone,  while  it  is  increased  by  the  use  of  a  bare  carbon  rod  dip- 
ping into  the  arc,  is  still  a  genuine  variation  of  the  carbon  P.Ds. 

In  other  words,  the  term  —  in  equation  (7)  and  ~-  in  equation 
A.  A 

(7)  show  genuine  changes  with  change  of  current  in  the  posi- 
tive carbon  P.D.  and  the  negative  carbon  P.D.  respectively. 

In  order  to  prove  this,  it  will  be  necessary  to  find  the 
equation  connecting  the  current  and  the  length  of  the  arc  with 
the  total  P.D.  across  the  carbons  when  the  third  carbon  is  in 
the  arc. 

It  has  been  mentioned  that  the  insertion  in  the  arc  of  a 
third  carbon  caused  the  P.D.  between  the  main  carbons  to  be 
increased  by  from  0'5  to  3  volts.  This  increase  is  usually 
rather  greater  with  the  third  carbon  near  the  positive  pole  than 
near  the  negative.  Tables  XXXIII.  and  XXXIV.  give  the 
actual  values  of  this  P.D.,  the  first  with  the  exploring  carbon 
near  the  positive,  and  the  second  with  it  near  the  negative 
pole. 

Equation  (8),  which  gives  the  sum  of  the  two  carbon  P.Ds., 
was  formed  from  equations  (6)  and  (7),  for  one  of  which  the 
third  carbon  was  near  the  positive  pole,  and  for  the  other  near 
the  negative.  In  order,  therefore,  to  be  able  to  compare 
equation  (8)  with  the  new  equation  for  the  total  P.D.  across 


P. I).   WITH  THIRD  CAliBON  IN  AEG. 


229 


Table  XXXIII. — P.D.  between  Main  Carious  with  point  of  Third 

Carbon  in  Arc  dose  to  Crater  of  Positive  Carbon. 
Solid  carbons.     Positive,  llmm.  ;  negative,  9mm.  ;  third  car- 
bon, 0-5mm.  to  2mm. 


Current 
in 
Amperes. 

P.D.  in  Volts. 

l-l. 

1  =  2. 

2=3. 

Z=4. 

1=5. 

2  =  6.       1  =  1. 

4 

48-3 

51-5 

571 

62-6 

66-4 

70-3 

5 

45-8 

51-3 

55-5 

60-7 

63-8 

67-3 

70-7 

6 

45-5 

50-6 

55-9 

58-5 

61-5 

64-5 

69-2 

7 

45-0 

50-5 

53-5 

57-4 

60-7 

63-9        67-4 

8 

44-0 

492 

52-4 

55-7 

59-6 

61-6        64-9 

9 

43-4 

47-9 

52-0 

54-4 

57-4 

60-6     ,    64-2 

10 

43-1 

47-5 

511 

54-4 

58-8 

60-7 

63-2 

12 

42-6 

46-7 

50-5 

53'0 

57-5 

58-9 

63-5 

14 

... 

46-0 

50-6 

51-8 

55-3 

58-7 

61-9 

16 

.... 

... 

... 

51-3 

551 

57-2 

60-6 

20 

... 

57-2        59-2 

Table  XXXIV. — P.D.  between  Main  Carbons  with  point  of  Third 

Carbon  in  Arc  dose  to  White  Not  Spot  on  Negative  Carbon. 
Solid  carbons.    Positive,  llmm.  ;  negative,  9mm.  ;  third  carbon, 
O'Smm.  to  2mm. 


Current 

P.D.  in  Volts. 

Amperes. 

1=1, 

1=2. 

2=3. 

2  =  4.    |    2  =  5. 

2  =  6. 

1=1. 

._ 

l 

I 

4 

49-5 

52-2 

57-2 

63-9 

68-3 

70-5 

5 

46-0 

51-5 

55-3 

60-5 

64-5 

68-3 

70-5 

6 

45-5 

50-7 

55-0 

588 

61-8 

65-5 

701 

7 

45-0 

50-5 

53-9 

57-3 

61-2 

655 

690 

8 

44-0 

48-7 

52-2 

55-7 

60-0 

61-6 

64-9 

9 

434 

49-2 

51-3 

54-5 

57-6 

61-2 

65-2 

10 

43-5 

47'3 

51-2 

54-7 

58-8 

607 

63'8 

12 

42-6 

46-7 

50-7 

53-5 

581 

59-3 

631 

14 

46-0 

51-5 

53-5 

56-6 

591 

60-6 

16 

511 

55-4 

57-3 

60-0 

20 

... 

... 

... 

58-0         59-3 

the  carbons  with  the  third  carbon  in  the  arc,  it  will  be  necessary 
that  this  new  equation  shall  connect  the  current  and  the  length 
of  the  arc  with  the  mean  of  the  total  P.Ds.  observed  when  the 
third  carbon  is  placed  near  the  positive  and  negative  carbons 
respectively.  That  is,  the  mean  of  each  P.D.  in  Table  XXXIII. 


230 


THE  ELECTEIC  AEG. 


and  the  corresponding  P.D.  in  Table  XXXIV.  must  be  taken  to- 
obtain  the  new  equation.  These  mean  P.Ds.  with  their 
respective  currents  and  lengths  of  arc  are  given  in  Table 
XXXV. 

Table  XXXV. — Mean  Total  P.D.  between  Main  Carbons  with 
Third  Carbon  in  Arc  near  Positive  and  Negative  Carbons- 
respectively. 

Solid  carbons.    Positive,  llmm.  ;  negative,  9mm.  ;  third  car- 
bon, 0'5mm.  to  2mm. 


P.D.  in  Volts. 

Current  in 

Amperes. 

1  =  1. 

1  =  2. 

£  =  3. 

Z=4. 

1=5. 

1=6. 

1=1. 

4 

48-9 

51-85 

57-15 

63-25 

67-35 

70-4 

5 

45-9 

51-4 

55-4 

60-6 

64-15 

67-8 

70-6 

6 

45-5 

50-65 

55-45 

58-65 

61-65 

65-0 

69-65 

7 

45-0 

50-5 

53-7 

57-35 

60-95 

64-7 

68-2 

8 

44-0 

48-95 

52-3 

55-7 

59-8 

61-6 

64-9 

9 

43-4 

48-55 

51-65 

54-45 

57-5 

60-9 

64-7 

10 

43-3 

47-4 

51-15 

54-55 

58-8 

60-7 

63-5 

12 

42-6 

46-7 

50-6 

53-25 

57-8 

59-1 

63-3 

14 

46-0 

51-05 

52-65 

55-95 

58-9 

61-25 

16 

51-2 

55-25 

57-25 

60-3 

20 

... 

... 

... 

... 

57-6 

59-25 

By  multiplying  each  of  the  P.Ds.  in  Table  XXXV.  by  the 
corresponding  current,  we  obtain  the  total  power  in  watts 
expended  between  the  carbons  when  the  third  carbon  is  in  the 
arc.  The  laws  connecting  this  power  with  the  current  for 
constant  length  of  arc  and  with  the  length  of  the  arc  for 
constant  current  are  both  straight  line  laws,  just  as  they  are 
when  there  is  no  third  carbon  in  the  arc  (p.  189).  By  com- 
bining these  two  laws  in  the  same  way  as  when  there  was  no 
third  carbon  we  get 


=  38-56 


(9) 


as  the  equation  representing  the  connection  between  P.D., 
current,  and  length  of  arc,  with  a  third  carbon  in  the  arc.  Of 
the  67  P.Ds.  calculated  from  this  equation,  59  differ  from 
the  observed  values  by  one  volt  and  under,  and  the  remaining 
8  by  less  than  1-7  volts.  These  calculated  P.Ds.  are  given  in 
Table  XXXVI. 


P  D.   WITH  TRIED  CARBON  IN  AEG. 


231 


Table  XXXVI. — Mean  P.Ds.  between  the  Main  Carbons  with 

Third  Carbon  in  the  Arc,  calculated  from  Equation  (9). 
Solid    carbons.       Positive,   llmm.  ;    negative,    9mm.  ;    third 
cnrbon,  0'5mm.  to  2mm. 


Current  in 

P.D..  in  Volts. 

Amperes. 

1  =  1. 

1=2. 

1  =  3. 

Z  =  4. 

1  =  5. 

1=6. 

1  =  7. 

4 

48-8 

53-3 

57-8 

62-3 

66-8 

71-3 

5 

4V3 

51-4 

55-5 

59-6 

63-7 

67-8 

71-9 

6 

46-2 

59-1 

53-9 

57-7 

61-5 

65-4 

69-2 

7 

45-5 

49-1 

52-8 

56-4 

60-1 

63-7 

67-4 

8 

44-9 

48-4 

51-9 

55-4 

58-9 

62-4 

65-9 

9 

44-5 

47-9 

51-3 

54-7 

58-0 

61-4 

64-7 

10 

44-2 

47-5 

50-8 

54-1 

67-3 

60-7 

64-0 

12 

43-6 

46-8 

50-0 

531 

56-3 

59-5 

62-6 

14 

4635 

49-4 

52-5 

55-6 

58-6 

61-7 

16 

... 

52-0 

55-0 

58-0 

61-0 

20 

... 

... 

... 

... 

57'1 

60-0 

To  see  how  the  disturbance  of  the  P.D.  caused  by  the 
presence  of  the  third  carbon  is  distributed,  we  must  compare 
equation  (9)  with  equation  (3)  for  which  there  was  no  third 
carbon  in  the  arc.  We  have 


V  =  38-56  +  '2- 


38-88  +  2-072  + 


11-66  +  10-542 


(9) 


(3) 


The  constant  terms  in  the  two  equations  may  be  considered 
to  be  identical,  since  there  is  only  0*32  volt  difference  between 
them.  Thus  the  third  carbon  does  not  interfere  with  this 
constant  term.  It  appears  to  increase  the  part  of  the  P.D. 
that  varies  with  the  length  alone,  and  to  diminish  that  which 
varies  with  both  length  and  current,  while  it  practically  doubles 
the  part  that  varies  with  the  current  alone. 

Let  us  now  compare  equation  (9)  with  equation  (8)  for  the 
sum  of  the  carbon  P.Ds  : 

V-  38-88  +  2 


and  we  find  that,  not  only  the  constant  terms,  but  also  those 
which  vary  with  the  current  alone  are  practically  identical. 
Hence,  leaving  out  the  small  variations  in  those  two  terms- 


232  THE  ELECTRIC  ARC. 

(which  probably  arise  from  experimental  errors),  we  find  that 
if  we  subtract  the  sum  of  the  two  carbon  P.Ds.  from  the  total 
P.D.  between  the  carbons,  we  have,  for  the  fall  of  potential 
through  the  carbon  vapour  itself,  two  terms,  of  which  one 
varies  with  the  length  of  the  arc  alone,  and  the  other  with 
both  the  current  and  the  length  of  the  arc,  but  no  term  varying 
with  the  current  alone.  It  seems,  therefore,  probable  that  that 
part  of  the  variation  in  the  positive  and  negative  carbon  P.Ds., 
which  depends  on  the  current  alone,  is  not  caused  solely  by  the 
use  of  a  bare  idle  carbon  in  the  arc,  but  is  a  true  variation 
which  takes  place  when  there  is  no  such  cause  of  disturbance, 
and  is  only  increased  by  the  insertion  of  the  rod.  In  other 

words,  the  term  ~~ ^—  in  equation  (3)  seems  really  to  belong 

to  the  carbon  P.Ds.,  which  are  not,  therefore,  constant  for  all 
currents. 

We  can  now,  with  tolerable  certainty,  locate  three  out  of 
the  four  terms  in  the  equation  which  connects  the  P.D.  across 
the  main  carbons  of  the  arc  with  the  current  and  the  length 
of  the  arc  (equation  3).  Apparently  the  first  and  third  terms 

•I  I  .Cf} 

38-88  +  —- —    belong  entirely  to  the  carbon  P.Ds.,   and  the 
A. 

second  term  belongs  entirely  to  the  vapour  P.D.  The  fourth 
term-— — is  more  difficult  to  locate;  part  of  it  certainly  belongs 


to  the  vapour  P.D.,  but  whether  any  of  it  really  belongs  to 
the  positive  carbon  P.D.,  as  equation  (6)  appears  to  show, 
or  whether  this  term  depends  entirely  on  the  use  of  the  bare 
third  carbon,  cannot  be  determined  without  fresh  experiments. 
So  far,  only  cases  (1)  and  (2)  of  Fig.  70  (p.  213)  have  been 
•discussed.  Tables  XXXVII.  and  XXXVIIL  give  the  P.Ds. 
found  when  the  experiments  represented  by  cases  (3)  and  (4) 
were  made.  Table  XXXVtI.  shows  the  P.D.  between  the  posi- 
tive carbon  and  the  third  carbon  just  before  it  touched  the 
negative  carbon,  for  each  length  of  arc  and  current.  That  is, 
the  positive  carbon  P.D.  plus  the  vapour  P.D.  Similarly, 
Table  XXXVIII.  gives  the  vapour  P.D.  plus  the  negative 
carbon  P.D.  for  each  length  of  arc  and  current.  These 
Tables  may  be  used  in  various  ways  to  confirm  the  deductions 
made  from  the  other  Tables  in  this  Chapter.  For  instance, 
if  the  corresponding  P.Ds.  in  each  of  Tables  XXXVII. 


CARBON  P.D.  PLUS  VAPOUR  P.D. 


233 


and  XXVIII.  be  added  together,  we  shall  get  the  total  P.D. 
across  the  main  carbons,  for  we  shall  have  added  the  negative 
carbon  P.D.  of  Table  XXVIII.  to  the  positive  carbon  P.D.  plus 
the  vapour  P.D.  of  Table  XXXVII.  As  both  these  sets  of 
P.Ds.  were  obtained  with  the  third  carbon  close  to  the  negative 
pole  (cases  (2)  and  (3),  Fig.  70,  p.  213),  their  sum  ought  to 
correspond  with  the  total  P.Ds.  across  the  main  carbons,  with 
the  third  carbon  in  the  same  position,  given  in  Table  XXXIV., 
except  that  the  increase  of  the  P.D.  caused  by  having  a  third 
carbon  in  the  arc  is  counte4  twice  over  in  Tables  XXVIII. 
and  XXXVII.  and  only  once  in  Table  XXX IV.  It  will  be 
found  that  agreement  between  the  two  sets  of  P.Ds.  is  so 
close1  that  43  of  the  pairs  of  values  differ  from  one  another 
by  less  than  one  volt,  and  the  remaining  18  by  less  than  two 
volts.  Again,  Table  XXXVIII.  may  be  used  in  the  same  way, 
in  conjunction  with  Tables  XXVII.  and  XXXIII.,  to  find 
indirectly  the  total  P.D.  across  the  carbons  with  the  third 
carbon  close  to  the  crater,  and  the  positive  carbon  P.D.  A 
comparison  of  these  with  the  corresponding  P.Ds.  obtained  by 
direct  observation  will  also  show  that  all  the  values  agree 
extremely  well  with  one  another,  though  not  quite  so  well  as 
the  experiments  made  with  the  third  carbon  near  the  negative 
pole,  because  the  arc  is  always  more  disturbed  when  the  third 
carbon  is  near  the  positive  pole. 

Table    XXXVII. — P.D.    between   Positive   Carbon  and   Third 

Carbon  with  Point  of  latter  close  to  White  Spot. 
Solid  carbons.    Positive,  llmm.  ;  negative^  9mm.  in  diameter  ; 
third  carbon,  0'5mm.  to  2mm.  in  diameter. 


P.D.  in  Volts. 

Current  in 

Amperes. 

1=1.    j    Z  =  2. 

Z=3, 

Z=4. 

1  =  5. 

1  =  6. 

1  =  7. 

4 

35-6 

39'8 

44-5 

52-3 

56-0 

60-8 

63-8 

5 

35-7 

41-4 

45-1 

50-1 

533 

57-8 

59-4 

6 

37-1 

401 

45-8 

49-6 

51-1 

55-0 

59-1 

7 

37-3 

40-9 

44-5 

4S-0 

51-0 

54-6 

57-6 

8 

36-2 

38-6 

41-5 

45-8     !     49-1 

50-8 

54-8 

9 

35-4 

40-3 

42-8 

43-9 

48-3 

50-9 

54-8 

10 

34-8 

38-7 

41-8 

45-4 

49-3 

51-4 

54-8 

12 

34-0 

38-0 

41-5 

44-6 

48-1 

49-5 

52-9 

14 

... 

36-1 

40-7 

44-7 

47-5 

49-7 

51-7 

16 

43-1 

47-0 

48-6 

51-3 

20 

... 

48-8 

50-4 

I 

234 


THE  ELECTEIC  ARC. 


Table  XXXVIII. — P.D.  between  Third  Carbon  and   Negative 

Carbon,  with  Point  of  latter  close  to  Crater. 
Solid  carbons.    Positive,  llmm.  ;  negative,  9mm.  in  diameter  ; 
third  carbon,  0'5mm.  to  2mm.  in  diameter. 


Current  in 
Amperes. 

JT.JU/.    Ill     VUll/O. 

Z=l. 

1=2. 

1=3. 

Z=4. 

1=5. 

1=6. 

1=1. 

4 

14-8 

14-1 

19-4 

24-9 

30-7 

30-5 

34-2 

5 

11-2 

193 

19-1 

24-4 

24-5 

28-9 

34-4 

6 

11-9 

159 

22-8 

21-9 

26-0 

29-8 

31-0 

7 

9-9 

17-7 

20-9 

25-8 

27-1 

27-5 

31-7 

8 

10-5 

15-5 

19-2 

20-7 

23-0 

28-4 

28-2 

9 

9-4 

15-6 

16-6 

19-7 

22-8 

24-1 

28-7 

10 

11-0 

15-3 

201 

20-4 

24-7 

27-5 

27-8 

12 

10-4 

14-2 

17-7 

20-8 

23-0 

25-2 

27-1 

14 

141 

17-8 

20-0 

21-9 

23-1 

26-8 

16 

... 

... 

... 

18-6 

20-6 

24-0 

28-0 

20 

... 

•• 

... 

... 

22-4 

26-3 

It  has  been  mentioned  that  four  series  of  experiments  were 
made  with  cored  carbons,  two  with  cored  positive  and  solid 
negative  carbons,  and  two  with  both  carbons  cored.  The 
results  of  these  experiments,  together  with  the  similar  results 
obtained  when  both  carbons  were  solid,  are  given  in  Tables 
XXXIX.  and  XLI. 

The  limited  number  of  the  experiments  with  cored  carbons 
renders  it  difficult  to  judge  of  the  effect  on  the  various  P.Ds* 
of  changing  the  current  and  the  length  of  the  arc,  as 
was  done  in  the  case  of  solid  carbons.  But  the  general 
result  of  substituting  cored  for  solid  carbons  is  easily 
seen,  especially  if,  instead  of  comparing  each  set  of  P.Ds, 
separately  with  one  another,  we  examine  the  average  P.Ds. 
given  at  the  end  of  each  series.  Thus  the  upper  part  of 
Table  XXXIX.  shows  that  with  both  carbons  solid  the  average 
total  P.D.  across  the  carbons  is  59 '9  volts,  while  with  the 
positive  carbon  cored  it  is  5 6 '8,  or  3*1  volts  less,  and  with 
both  cored  it  is  54%1  volts,  or  5'S  volts  less  than  with  both 
carbons  solid.  Hence,  coring  either  carbon  diminishes  the 
total  P.D.,  but  the  diminution  of  P.D.  is  almost  twice  as 
great  with  both  carbons  cored  as  it  is  with  the  positive 
carbon  alone  cored,  with  an  arc  of  5mm.  With  a  current  of 
10  amperes  and  various  lengths  of  arc  the  diminution  in  the 


CORED  CARBONS. 


235 


average  total  P.D.  is  exactly  twice  as  great  when  both  carbons 
are  cored  as  when  the  positive  alone  is  cored,  as  is  seen  from 
the  lower  part  of  Table  XXXIX. 

Table  XXXIX. — Comparison,  with  Gored  and  Solid  Carbons,  of 

P.D.  between  the  Carbons  with  a  Third  Carbon  in  the  Arc. 
Positive    carbon,    llmm. ;    negative,    9mm. ;     third    carbon, 
0'5mm.  to  2mm. 

Length  of  Arc,  5mm. 


Current 

P.D.  between  Carbons  in  Volts. 

• 

Amperes. 

Both  solid. 

+  Cored,  -Solid. 

Both  Cored. 

4 

67-35 

65-6 

62-5 

5 

64-15 

59-9 

57-8 

6 

61-65 

57-3 

54-8 

7 

60-95 

57-6 

54-0 

8 

59-8 

55-9 

53-7 

9 

57-5 

55-6 

53-6 

10 

58-8 

54-2 

53-2 

12 

57-8 

53-9 

50-9 

14 

55-95 

54-2 

50-3 

16 

5525 

53-7 

50-0 

Average. 

59-9 

56-8 

54-1 

Current,  10  Amperes. 


Length  of  Arc 

P.D.  between  Carbons  in  Volts. 

Millimetres. 

Both  Solid. 

+  Cored,  -Solid. 

Both  Cored. 

1 

43-3 

43-4 

39-9 

2 

47-4 

45-3 

43-8 

3 

51-15 

50-0 

486 

4 

54-55 

53-4 

51-0 

5 

58-8 

54-2 

53-2 

6 

60-7 

57-5 

65-3 

7 

63-5 

59-7 

55-7 

Average 

54-2 

51-9 

49-6 

The  important  thing  to  find  out  about  this  diminution  of 
P.D.  is  whether  it  takes  place  in  either  of  the  carbon  P.Ds.  or 
both,  or  in  the  vapour  P.D.  Table  XL.  shows  that  a  certain 
amount  of  it  takes  place  in  the  positive  carbon  P.D.,  but  not  all, 
even  when  the  positive  carbon  alone  is  cored,  for  although  the 


236 


THE  ELECTRIC  AEC. 


average  positive  carbon  P.D.  is  reduced  by  3'3  volts,  by  the 
use  of  a  cored  positive  carbon,  which  is  about  the  same  as  the 
reduction  in  the  total  P.D.,  with  an  arc  of  5mm.,  yet  with  a 
current  of  10  amperes  the  average  positive  carbon  P.D.  is 
reduced  by  1*3  volts  by  coring  the  positive  carbon,  whereas 
the  average  total  P.D.  is  reduced  by  2 -3  volts.  Hence  it  is 
probable  that  part  of  the  reduction  in  the  total  P.D.  is  caused 
by  the  carbon  vapour  itself  being  rendered  more  conducting 
by  the  presence  of  the  vapour  from  the  core. 

Table   XL. — Comparison,   with    Cored  and  Solid  Carbons,   of 

Positive  Carbon  P.Ds. 

Positive    carbon,    llmm. ;    negative,    9mm. ;    third    carbon, 
0'5mm.  to  2mm. 

Length  of  Arc,  5mm. 


Current 

P.D.  in  Volts. 

in. 

Amperes. 

Both  Solid. 

+  Cored,  -  Solid. 

Both  Cored. 

4 

36-7 

31-2 

36-9 

5 

35-5 

3L-0 

32-5 

6 

3555 

31-1 

311 

7 

35-0 

29-7 

31-3 

8 

34-9 

34-4 

31-6 

9 

35-4 

29-2 

31  -8 

10 

33-5 

31-8 

32-5 

12 

338 

30-8 

30-7 

14 

31-8 

310 

339 

16 

32-7 

32-0 

31-2 

Average 

34-5 

31-2 

32-3 

Current,  10  Amperes. 


Length  of  Arc 
in 
Millimetres. 

P.D.  in  Volts. 

Both  Solid. 

+  Cored,  -Solid. 

Both  Cored. 

1 
2 
3 
4 
5 
6 
7 

32-6 
32-4 
31-5 
33-75 
335 
32-7 
34-7 

34-0 
31-2 
31-6 
32-4 
31-8 
31-0 
30-2 

31-2 
33-4 
33-7 
34-3 
32-5 
31-9 
321 

Average 

33-0 

31-7 

32-7 

CORED  CARBONS. 


237 


With  both  carbons  cored  the  loss  in  the  positive  carbon  P.D. 
appears  to  be  less  than  when  the  positive  alone  is  cored,  but 
this  is  probably  only  an  apparent  difference  caused  by  the  core 
being  harder  in  the  one  case  than  in  the  other.  We  may,  I 

Table  XLI. — Comparison,  with  Cored  and  Solid  Carbons,   of 

Negative  Carbon  P.Ds. 

Positive  carbon,  llmm. ;  negative,  9mm. ;  third  carbon, 
0-5mm.  to  2mm. 

Length  of  Arc,  5mm. 


Current 

P.D.  in  Volts. 

in 
Amperes. 

Both  Solid. 

+  Cored,  -Solid. 

Both  Cored. 

4 

104 

101 

10-6 

5 

10-8 

8-9 

9-2 

6 

9'7 

8-5 

9-3 

7 

9-4 

8-6 

8-6 

8 

10-0 

8-5 

7-6 

9 

9-6 

8-6 

9-0 

10 

9-2 

8-5 

9-0 

12 

9-6 

8-5 

9-1 

14 

9-2 

8-7 

7-9 

16 

9-2 

8-8 

81 

Average 

9-6 

8-8 

8-8 

Current,  10  Amperes. 


Length  of  Arc 

P.D.  in  Volts. 

Millimetres. 

Both  Solid. 

+  Cored,  -Solid. 

Both  Cored. 

1 

8-5 

8-0 

7-8 

2 

8-5 

8-8 

8'9 

3 

9-0 

8-8 

8-5 

4 

8-9 

8-6 

8-7 

5 

9-2 

8-5 

9-0 

6 

9-2 

8-7 

9-0 

7 

9-2 

8-7 

8-6 

Average                         8'9 

86 

8-6 

think,  take  it  for  granted  that,  other  things  being  the  same, 
the  reduction  of  the  positive  carbon  P.D.  caused  by  coring  is 
about  the  same,  whether  the  negative  carbon  is  cored  or  solid. 
Hence  the  increased  reduction  of  the  total  P.D.  caused  by 


238  THE  ELECTRIC  AEG. 

coring  the  negative  carbon  must  be  the  result  of  a  reduction 
either  of  the  vapour  P.D.  or  of  the  negative  carbon  P.D.,  or  of 
both.  That  it  is  not  in  the  negative  carbon  P.D.  that  the 
reduction  takes  place  may  be  seen  from  Table  XLL,  for,  with  the 
positive  carbon  cored,  the  average  negative  carbon  P.D.  appears 
to  be  the  same,  whether  the  negative  carbon  be  cored  or  not. 
Hence  it  appears  that  while  coring  the  positive  carbon  reduces 
both  the  positive  carbon  P.D.  and  the  vapour  P.D.,  coring  the 
negative  carbon  only  further  reduces  the  vapour  P.D. 

The  reduction  of  the  positive  carbon  P.D.  is  probably  due  to 
the  ease  with  which  the  core  vapourises  compared  with  the 
solid  carbon.  The  reduction  of  the  vapour  P.D.  mubt  be 
caused  by  the  vapour  of  the  core  having  greater  conductivity 
than  that  of  the  solid  carbon.  The  conductivity  must  indeed 
be  very  much  greater,  for,  as  was  mentioned  in  Chapter  I. 
(p.  16),  the  visible  cross  section  of  the  arc  is  always  less  for 
the  same  current  and  length  of  arc,  with  a  cored  than  with  a 
solid  positive  carbon,  and  hence,  all  other  things  being  equal, 
the  P.D.  required  to  send  a  given  current  would  be  greater  and 
not  less  with  the  cored  carbon. 

It  may  be  mentioned  that  a  cored  negative  carbon  always 
develops  a  deep  crater  just  as  if  it  were  a  positive  carbon. 


SUMMARY. 

SOLID  CARBONS. 

I.  The  positive  carbon  P.D.  increases  as  the  length  of  the 
arc  increases,  and  diminishes  as  the  current  increases. 

TI.  The  negative  carbon  P.D.  does  not  vary  with  the  length 
of  the  arc,  but  diminishes  as  the  current  increases.  The  fall 
of  potential  at  the  junction  of  this  carbon  with  the  arc  is 
always  from  arc  to  carbon,  and  nevar  in  the  opposite  direction. 

III.  In  the  equations  connecting  each  of  the  carbon  P.Ds. 
with  the  current  and  the  length  of  the  arc,  there  is  a  constant 
term.  The  sum  of  these  two  constant  terms  has  the  same 
value  as  the  constant  term  (commonly  called  the  back  E.M.F. 
of  the  arc)  in  the  equation  connecting  the  total  P.D.  across  the 
carbons  with  the  current  and  the  length  of  the  arc. 


SUMMARY.  239 

IV.  Hence,  a  part  of  this  so-called  back  E.M.F.  belongs  to  the 
negative  carbon  P.D.,  and  only  about  four  fifths  of  it  to  the 
positive  carbon  P.D.  instead  of  the  whole,  as  has  hitherto  been 
supposed. 

V.  The  term  involving  the  current  alone  in  the  total  P.D. 
equation  belongs  to  the    two    carbon    P.Ds.,    and  the  term 
involving    the    length    of    the    arc    alone    belongs    to    the 
vapour  P.D. 

CORED  CARBONS. 

VI.  The  reduction  of  the  total  P.D.,  caused  by  using  cored 
instead  of  solid  carbons,  is  made  partly  in  the  positive  carbon 
P.D.,  and  partly  in  the  vapour  P.D.     Very  little  of  it  is  made 
in  the  negative  carbon  P.D.,  even  when  the  negative  carbon  is 
cored. 


CHAPTER    VIII. 


THE  KELATIONS  EXISTING  BETWEEN  THE  E.M.F.  OP  THE 
GENERATOR,  THE  RESISTANCE  IN  THE  CIRCUIT  OUTSIDE  THE 
ARC,  THE  LENGTH  OP  THE  ARC,  THE  CURRENT  AND  THE  P.D. 

BETWEEN  THE  CARBONS  WITH  SOLID  CARBONS. 

Hitherto  the  arc  alone  has  been  considered,  without  any 
reference  to  the  E.M.F.  of  the  generator,  or  the  resistance 
placed  in  circuit  outside  the  arc.  The  influence  on  the  arc 
of  any  change  in  either  of  these  may  be  studied  in  two  ways, 
graphically,  by  means  of  Fig.  79,  the  curves  in  which  are  a 
reproduction  of  those  in  Fig.  38,  with  certain  additions ;  and 
analytically,  by  examining  equation  (4)  (p.  186),  in  conjunction 
with  an  equation  expressing  the  relation  between  the  E.M.F. 
of  the  generator,  the  P.D.  between  the  ends  of  the  carbons, 
the  outside  resistance  in  circuit,  and  the  current  flowing. 

The  graphical  method  is,  perhaps,  the  easier  to  follow,  and 
may,  therefore,  be  taken  first.  Let  P  (Fig.  79)  be  a  point  on  the 
axis  of  P.D.  such  that  its  distance  from  the  axis  of  current 
represents  the  E.M.F.  in  volts  of  the  generator  supplying  the 
current,  and  let  P  Q  be  a  line  parallel  to  the  axis  of  current,  so 
that  the  distance  of  any  point  on  P  Q  from  the  axis  of  current 
will  represent  this  same  E.M.F.  Then,  if  Rx  be  a  point  on  one 
of  the  curves,  the  distance  between  Rj  and  the  axis  of  current 
will  represent  the  P.D.  in  volts  used  in  sending  the  current 
through  the  arc,  and  Rx  S,  the  distance  between  Rj  and  P  Q, 
will  represent  the  P.D.  employed  in  sending  the  current 
through  the  whole  of  the  resistance  outside  the  arc.  Also, 
since  PS  represents  the  current  flowing  when  that  outside 
resistance  is  in  circuit,  the  ratio  of  S  Rx  to  S  P,  which  is  tan. 
R!  P  Q,  represents  this  outside  resistance. 

If,  then,  with  the  given  generator  supplying  the  current,  any 
line  be  drawn  from  P  making  an  angle  Q  P  R  with  P  Q,  and 
cutting  the  curves  at  various  points,  the  positions  of  those  points 


242 


THE  ELECTEIC  AEC. 
Both  Carbons  Solid. 


ALTERING  CONDITIONS  OF  ARC.  243 

will  represent  the  relation  between  P.D.  and  current  in  arcs 
all  supplied  by  a  generator  with  the  same  E.M.F.,  and 
all  having  the  same  outside  resistance  in  circuit — namely,  that 
represented  by  the  tangent  of  the  angle  R  P  Q.  We  may 
then,  for  convenience  sake,  call  such  lines  as  P  RjY  resistance 
lines. 

There  are  three  possible  ways  of  altering  the  conditions  of 
the  arc  when  the  E.M.F.  of  the  generator  is  kept  constant, 
viz. : — 

(1)  The  external  resistance  may  be  kept  constant,  and  the 
length  of  the  arc  varied. 

(2)  The  length  of  the  arc  may  be  kept  constant,  and  the 
external  resistance  varied. 

(3)  Both  the  external  resistance  and  the  length  of  the  arc 
may  be  varied  together. 

In  the  first  case,  since  everything  is  constant  except  the 
length  of  the  arc,  lengthening  the  arc  must  mean  increasing 
the  resistance  in  the  whole  circuit,  and  consequently  a  diminu- 
tion of  current  must  follow  on  it.  Similarly,  shortening  the 
arc  must  mean  a  diminution  of  the  total  resistance  in  circuit, 
and  therefore  an  increase  of  current  must  follow  on  it. 

In  the  second  case,  since  everything  is  constant  except  the 
external  resistance,  increasing  this  must  increase  the  total 
resistance  in  circuit,  and  therefore  must  diminish  the  current ; 
while  diminishing  the  external  resistance  must  cause  a  diminu- 
tion in  the  total  resistance  in  circuit,  and  therefore  must  cause 
an  increase  in  the  current. 

In  the  third  case,  the  current  may  be  made  to  vary  in  any 
manner  that  is  desired,  or  to  remain  constant,  by  suitable 
variations  of  the  external  resistance  and  the  length  of  the  arc. 
But  the  sum  of  the  effects  of  the  variation  of  each  of  these 
must  be  the  same  as  if  each  had  been  varied  separately  while 
the  other  was  kept  constant,  so  long  as  one  of  the  variations 
does  not  cause  the  arc  to  be  extinguished,  thus  making  it 
impossible  for  the  other  to  take  effect  after  it. 

While  the  external  resistance  can  really  be  kept  absolutely 
constant,  the  length  of  the  arc  cannot,  for  it  is  quite  impossible, 
either  automatically  or  by  hand,  to  keep  the  carbons  moving 
towards  each  other  at  exactly  the  same  rate  at  which  they 
burn  away.  Consequently  what  is  called  keeping  the  length 


244  THE  ELECTRIC  ARC. 

of  arc  constant  is  really  allowing  it  to  become  slightly  longer 
than  the  desired  length,  and  then  bringing  the  carbons  together 
till  it  is  slightly  shorter,  so  that  the  curve  connecting  time  and 
length  of  arc  when  the  length  of  arc  was  supposed  to  be  con- 
stant, would  be  a  zig-zag,  not  a  straight  line. 

Similarly,  what  is  called  a  constant  current  is  not  really  con- 
stant, for  it  is  impossible  to  lengthen  or  shorten  the  arc,  and 
at  the  same  time  alter  the  resistance  by  exactly  the  right 
amount  to  keep  the  current  constant.  Hence  there  is  a  con- 
tinual increase  and  decrease  of  current  above  and  below  the 
supposed  constant  value.  Nevertheless  it  is  possible  to  keep 
both  length  of  arc  and  current  constant  within  certain  limits, 
which  may  be  made  very  narrow  by  careful  experimenting. 

If  we  follow  one  of  the  resistance  lines,  P  RjY,  for  instance, 
we  shall  see  what  happens  when  the  external  resistance  is  kept 
constant,  and  the  length  of  the  arc  varied. 

The  first  thing  that  strikes  one  about  this  line  is  that  the 
curves  for  silent  arcs  above  a  certain  length — viz.,  6mm. — are 
not  cut  by  it  at  all ;  that  the  curve  for  this  length  is  touched 
by  the  line,  while  those  for  shorter  lengths  of  arc  are  cut  by  it 
in  two  points,  or  would  be  cut  in  two  points,  if  hissing  did  not 
intervene  and  terminate  the  curve.  The  two  points  at  which 
the  line  P  RXY  cuts  each  of  the  curves  for  lengths  of  arc  less 
than  6mm.  are  closer  together  the  nearer  the  length  of  the  arc 
is  to  6mm.,  and  we  may  consider  that  it  really  cuts  the  6mm. 
curve  at  two  points  which  are  coincident.  The  fact  of  its  not 
cutting  the  curves  for  longer  arcs  at  all  shows  that  no  arc  of 
greater  length  than  6mm.  can  be  maintained  by  a  generator 
with  the  given  constant  E.M.F.  when  a  resistance  represented 
by  tan  RtP  Q  is  in  the  circuit  outside  the  arc ;  in  other  words, 
6mm.  is  the  maximum  length  of  arc  that  can  be  maintained 
under  the  given  conditions  of  generator  and  external  resistance. 

From  the  resistance  lines  cutting  each  of  the  curves 
that  they  meet  at  two  points  it  would  appear  as  if,  with  a 
generator  of  constant  E.M.F.,  and  a  constant  resistance  in 
circuit  external  to  the  arc,  two  widely  different  currents  might 
be  sent  through  two  arcs  of  the  same  length.  That  is, 
apparently,  under  two  precisely  similar  sets  of  conditions,  two 
entirely  different  things  may  happen.  This  is,  of  course, 
absurd.  Either  the  conditions  cannot  be  precisely  similar, 


RESISTANCE  LINES.  245 

or,  if  they  are,  the  two  different  currents  cannot  permanently 
flow.  By  tracing  the  course  of  events  from  the  moment  the 
arc  is  struck  it  is  possible  to  find  out  which  of  these  two 
hypotheses  is  justified  by  facts. 

We  know  from  experience  that,  immediately  after  striking 
the  arc,  in  the  ordinary  way,  the  current  flowing  is  compara- 
tively large,  since  the  length  of  the  arc  is  very  small,  and  that 
if  we  lengthen  the  arc  without  altering  the  resistance  in 
circuit,  we  diminish  the  current.  Hence  it  is  evident  that  if 
we  want  to  follow  the  course  of  events  after  striking  the  arc, 
we  must  start  from  the  right  hand  point  of  intersection  with 
the  shortest  length  of  arc,  and  follow  the  line  P  RjY  from  right 
to  left,  because  we  then  arrive  successively  at  points  of  inter- 
section which  show  that  the  current  diminishes  as  the  length 
of  the  arc  increases.  For  instance,  following  P  RjY  (which 
corresponds  with  an  E.M.F.  of  68'88  volts  and  an  external 
resistance  of  1'05  ohms)  from  right  to  left,  we  see  that  when 
the  arc  is  4mm.  in  length  the  current  is  about  18  amperes, 
when  it  is  5mm.  the  current  is  about  14  amperes,  and  when  it 
is  6mm.  the  current  is  a  little  over  8  amperes.  But  if  we  start 
from  the  left  hand  point  of  intersection  with  the  shortest  length 
of  arc,  and  follow  the  line  PRXY  from  left  to  right,  we  arrive 
successively  at  points  of  intersection  which  show  that  the  current 
increases  as  the  length  of  the  arc  increases.  The  right-hand 
points  of  intersection  of  the  resistance  lines  with  the  curves 
are,  then,  those  we  are  accustomed  to  find  after  striking  an  arc, 
and  we  know,  therefore,  that  they  are  possible.  Can  the  left- 
hand  points  also  be  obtained  when  the  E.M.F.  of  the  generator 
and  the  outside  resistance  are  the  same  as  for  the  right-hand 
points?  is  the  question  now  to  be  answered. 

In  going  from  right  to  left  along  the  line  P  I^Y,  everything 
is  perfectly  easy  till  the  arc  is  6mm.  in  length,  that  is,  till  the 
resistance  line  is  a  tangent  to  the  curve  connecting  P.D.  and 
current.  When  this  point  is  reached,  however,  trouble  arises, 
for,  since  6mm.  has  been  shown  to  be  the  maximum  length  of 
arc  that  it  is  possible  to  maintain  with  the  given  resistance  in 
circuit,  and  since  the  tendency  of  the  arc  is  to  lengthen, 
unless  the  carbons  are  brought  nearer  together  at  the  very 
moment  they  have  become  6mm.  apart,  the  arc  will  be  ex- 
tinguished. 


246  THE  ELECTRIC  ARC. 

It  would,  of  course,  be  very  difficult,  if  not  impossible,  to 
bring  the  carbons  nearer  together  at  the  precise  moment  when 
their  distance  apart  was  6mm.,  but  supposing  that  done,  the 
question  arises,  which  course  would  the  point  of  intersection  of 
the  resistance  line  and  the  curve  for  the  shorter  arc  take ; 
would  it  move  to  the  right  or  to  the  left,  should  we  get  a  right- 
hand  or  a  left-hand  point  of  intersection  between  the  resistance 
line  and  the  curve ;  or,  in  other  words,  would  the  current 
increase  or  diminish  1  There  is  not  much  difficulty  in  answer- 
ing that  question.  It  has  already  been  pointed  out  that,  if 
everything  else  remains  unchanged,  shortening  the  arc  can 
have  only  one  result:  it  must  lessen  the  total  resistance  in 
circuit,  and  therefore  lead  to  an  increase  of  current. 

Hence  the  point  Rx  will  move  to  the  right  when  the  arc 
is  shortened,  and  it  is  thus  evident  that  it  is  not  possible 
to  obtain  a  left-hand  point  of  intersection  between  the  resis- 
tance line  and  the  curve  by  keeping  the  external  resistance  con- 
stant and  varying  the  length  of  the  arc. 

It  still  might  be  possible,  however,  to  get  to  a  left-hand 
point  of  intersection  by  varying  the  external  resistance  and 
keeping  the  arc  at  a  constant  length.  Let  us  see.  We  may 
suppose  that  the  arc  has  been  struck,  that  its  length  has  been 
increased  from  zero  to  6mm.,  and  that  a  silent  arc  is  being 
maintained  with  a  current  of  about  20  amperes  flowing.  If  the 
length  of  the  arc  be  now  kept  constant  the  external  resistance 
will  have  to  be  increased,  in  order  that  we  may  pass  along  the 
curve  for  a  silent  arc  of  6mm.  As  the  resistance  is  increased  the 
current  will  diminish,  and  the  points  of  intersection  between 
the  resistance  lines  and  the  curve  will  be  right-hand  points, 
such  as  R4  and  R5,  till  the  resistance  is  represented  by 
tan  RjP  Q,  and  the  resistance  line  is  a  tangent  to  the  curve. 

When  that  moment  is  reached  the  resistance  has  of  course 
gained  its  maximum  value  for  a  6mm.  arc,  for  if  the  angle 
R^Q  were  still  further  increased,  the  line  Rx  P  would  not 
meet  the  6mm.  curve  at  all.  Hence,  at  this  point,  the  resis- 
tance must  be  diminished  the  moment  the  arc  is  6mm.  long, 
and  the  question  again  arises,  Which  way  would  the  point 
E,  go — to  the  right  or  the  left  1  Would  the  current  increase 
or  diminish  when  the  external  resistance  was  diminished? 
This  question  is  readily  answered.  We  know  that  diminishing 


UNSTABLE  CONDITIONS.  247 

the  resistance,  and  leaving  all  else  unchanged,  can  only  cause 
a  diminution  in  the  total  resistance  in  circuit,  and  hence  an 
increase  of  current,  which  will  give  us  over  again  points  on 
the  curve  to  the  right  of  R^  It  is,  therefore,  impossible  to 
obtain  the  left-hand  points  of  intersection  between  the  resis- 
tance lines  and  the  curves  by  varying  the  external  resistance 
and  keeping  the  length  of  the  arc  constant. 

It  remains  only  now  to  see  if  these  points  can  be  obtained 
by  varying  both  the  external  resistance  and  the  length  of  the 
arc  at  the  same  moment,  and  this  seems  the  most  plausible 
method  of  all.  It  seems  so  possible,  when  the  resistance  line 
is  just  about  to  become  a  tangent  to  the  curve,  to  suddenly 
diminish  the  resistance  and  lengthen  the  arc  at  the  same  moment, 
so  as  to  pass  quickly  through  the  critical  point,  and  arrive  safely 
at  a  left-hand  point  of  intersection  on  the  other  side  of  it. 

That  this  idea  is  fallacious  is,  however,  easily  proved  by 
referring  to  three  conclusions  that  have  already  been  shown 
to  be  true.  With  a  generator  of  constant  E.M.F.  to  supply 
the  current — 

(1)  Changing  both  the  length  of  the  arc  and  the  resistance 
together   can  only  have    the  same    effect   as   changing    each 
separately  in  quick  succession,  if  the  order  of  change  be  such  that 
one  does  not  extinguish  the  arc  before  the  other  can  take  effect. 

(2)  Changing  the  length  of  the  arc  alone  can  give  only  right- 
hand  points  of  intersection  between  the  resistance  lines  and  the 
curves. 

(3)  Changing  the  resistance  alone  can  give  only  right-hand 
points  of  intersection  between  the  resistance  lines  and  the  curves. 

From  these  three  facts  it  follows  that  it  is  impossible  to 
obtain  left-hand  points  of  intersection  between  the  resistance 
lines  and  the  curves  by  altering  the  external  resistance  and  the 
length  of  the  arc  simultaneously,  and  it  follows  that  there  is  no 
possible  way  of  varying  the  conditions  of  the  arc  in  such  a 
manner  as  to  obtain  left-hand  points  of  intersection  between  the 
resistance  lines  and  the  curves  connecting  P.D.  and  current. 

Hence  no  points  can  be  obtained  on  the  curves  connecting 
P.D.  and  current  farther  to  the  left  than  those  which  form  the 
points  of  contact  between  the  curves  and  the  tangents  drawn 
to  the  curves  from  that  point  on  the  axis  of  P.D.  which 
indicates  the  E.M.F.  of  the  generator. 


248  THE  ELEGTEIG  AEG. 

It  follows,  therefore,  that  if  P  be  a  point  on  the  axis  of  P.D. 
such  that  its  distance  from  the  axis  of  current  represents  the 
E.M.F.  of  the  generator,  and  if  PR  be  the  tangent  through  P 
to  the  P.D.  and  current  curve  for  an  arc  of  given  length  at  the 
point  indicating  the  given  current,  then  the  given  E.M.F.  is 
the  smallest  that  can  be  used  to  supply  that  length  of  arc  and 
current.  This  was  first  pointed  out  by  M.  Blondel  in  1891 
(see  p.  62). 

The  question  arises,  How  can  the  left-hand  points  be 
obtained  at  all ;  how  were  they  obtained  ?  They  were  obtained 
as  right-hand  points,  by  using  a  generator  with  a  much  larger 
E.M.F.  than  that  indicated  by  the  position  of  P.  It  is,  of 
course,  obvious  that  all  the  points  on  the  curves  that  are  higher 
up  than  the  line  P  Q  must  have  been  obtained  with  a  generator 
of  larger  E.M.F.  than  that  indicated  by  P;  but  what  this 
investigation  shows  is  that  some  of  the  points  that  are  much 
lower  down  in  the  figure  than  the  line  P  Q  must  also  have  had 
a  generator  of  higher  E.M.F.  to  produce  them.  The  point  for 

2  amperes,  for  instance,  on  the  2mm.  curve,  although  corres- 
ponding with  a  P.D.  of  only  58'5  volts,  must  have  been  found 
with  a  larger  E.M.F.  than  69  volts,  which  is  indicated  by  the 
position  of  P,  for  the  tangent  from  Pto  the  2mm.  curve  touches 
the  curve  at  a  point  indicating  a  current  of  between  2  and 

3  amperes. 

On  referring  to  Fig.  79,  it  is  seen  that  a  left-hand  point  of 
intersection  of  a  resistance  line  and  a  curve — for  example,  the 
left-hand  point  T',  where  the  resistance  line  Rx  P  meets  the 
5mm.  curve — has  the  following  property  :  If  the  E.M.F.  of  the 
generator  be  kept  constant,  and  also  the  length  of  the  arc,  an 
increase  of  the  resistance  of  the  circuit  corresponds  with  an 
increase  of  the  current.  Now,  this  is  exactly  the  condition  of 
the  unstable  solution  that  is  obtained  when  a  series  dynamo, 
running  at  fixed  speed,  is  in  series  with  a  set  of  accumulators  of 
fixed  E.M.F.,  the  total  resistance  in  circuit  being  also  fixed. 

For  in  such  a  case,  as  the  late  Dr.  J\  Hopkinson  showed  some 
years  ago,  there  are  three  distinct  values  of  the  current  possible, 
two  of  these  corresponding  with  the  dynamo  charging  the  cells, 
while  the  third,  which  is  very  large  and  is  negative,  is  produced 
when  the  magnetisation  of  the  dynamo  has  been  reversed,  and 
the  dynamo  is  helping  the  cells  to  discharge.  Now,  the  smaller  of 


LARGE  E.M.F.  FOR  SMALL  CURRENTS.     249 

the  two  positive  charging  currents  is  unstable,  for  it  increases  in 
value  with  an  increase  of  the  resistance  in  circuit,  so  that  on 
the  slightest  change  in  the  speed  of  the  dynamo,  or  in  the 
resistance  in  circuit,  this  unstable  current  is  suddenly  changed 
into  the  larger  charging  current,  or  into  the  very  much  larger 
discharging  current. 

Further,  just  as  I  have  shown  that  a  left-hand  point  in 
Fig.  79  may,  for  the  same  current  and  length  of  arc,  be  changed 
into  a  right-hand  one  by  increasing  the  E.M.F.  of  the  generator 
and  the  resistance  in  circuit,  so  it  may  be  shown  that  Dr.  Hop- 
kinson's  unstable  point  may,  for  the  same  current  and  the  same 
set  of  accumulators,  be  changed  into  a  stable  solution  by  raising 
the  speed  of  the  series  dynamo  and  increasing  the  resistance  in 
circuit. 

The  impossibility  of  obtaining  small  currents  without  having 
a  comparatively  large  E.M.F.  in  the  generator  and  a  large 
external  resistance,  explains  a  very  puzzling  circumstance  that 
occurred  in  carrying  out  the  experiments  of  which  the  curves 
in  Fig.  79  are  the  result — one  which  many  other  experi- 
menters must  also  have  noticed, 

There  were  two  dynamos  at  the  Central  Technical  College, 
either  of  which  it  was  convenient  for  me  to  use ;  one  of  these 
produced  about  120  volts,  and  the  other  about  150  volts  on 
open  circuit.  The  first  ran  much  more  steadily  than  the 
second,  which  was  driven  by  a  single-cylinder  engine ;  the 
former  was,  therefore,  much  better  to  employ  in  a  general 
way;  when,  however,  it  was  used  for  small  currents  and  long 
arcs,  the  arc  behaved  in  the  most  tricky  manner,  going  out 
again  and  again  for  no  apparent  cause. 

The  reason  of  this  is  now  obvious.  The  curves  for  long  arcs 
are  so  nearly  vertical  in  the  parts  for  small  currents,  that  the 
tangents  to  those  curves  at  any  of  the  points  indicating  small 
currents  are  very  nearly  parallel  to  the  axis  of  P.D.,  and  there- 
fore intersect  it  very  high  up.  It  is  this  point  of  intersection, 
however,  that  determines  the  smallest  E.M.F.  that  it  is  possible 
to  have  in  the  generator,  and  the  smallest  resistance  that  it  is 
possible  to  have  in  the  circuit,  in  order  that  a  given  current 
shall  flow  through  a  given  length  of  arc.  Thus,  although,  for 
the  smallest  current  and  longest  arc  I  used,  a  P.D.  of  only  about 
86  volts  was  required  for  the  arc  itself,  yet  an  E.M.F.  of 


250  THE  ELECTRIC  ARC. 

considerably  over  120  volts  was  needed  in  the  generator  to 
enable  the  arc  to  be  maintained  at  all  with  the  given  small 
current  flowing.  The  remainder  of  this  large  E.M.F.  had  to  be 
wasted  in  sending  the  current  through  the  large  resistance  that 
it  was  absolutely  necessary  to  have  in  circuit. 

Thus  the  resistance  added  to  an  arc  lamp  on  a  constant- 
pressure  circuit  fulfils  three  distinct  functions.  It  prevents 
an  enormous  current  flowing  when  the  arc  is  first  struck ;  it 
renders  it  possible  for  a  solenoid  placed  in  series  with  the  arc 
to  regulate  its  length  ;  and  we  now  see  that  with  solid  carbons 
this  resistance  fulfils  a  third  and  entirely  different  function,  for 
without  some  resistance  being  placed  in  the  circuit  external  to  the 
arc  it  is  impossible  to  maintain  a  silent  arc  at  all. 

Hence  the  resistance  placed  in  series  with  an  arc  lamp  "  to  steady 
the  arc,"  as  is  commonly  said,  fulfils  the  all-important  function 
of  making  a  silent  arc  possible. 

In  fact,  an  arc  possesses  this  very  curious  property, 
viz.  :  that,  although  a  certain  current  of,  say,  A  amperes 
flowing  steadily  through  an  arc  of,  say,  I  mm.  corresponds  with 
a  P.D.  of,  say,  V  volts  between  the  carbons,  the  mere  mainten- 
ance of  this  P.D.  of  V  volts  between  the  carbons  with  the  arc 
of  I  mm.,  is  not  a  sufficient  condition  to  ensure  that  the  current 
of  A  amperes  shall  continue  to  flow.  There  must  also  be  a 
resistance  in  the  circuit  outside  the  arc,  which  can  not  have 
less  than  a  certain  minimum  value. 

As  an  example  of  this  peculiarity,  I  may  refer  to  the  difficulty, 
alluded  to  on  page  170,  which  I  met  with  when  experimenting 
on  arcs  with  constant  P.Ds.  An  examination  of  Fig.  79  shows 
that  when,  for  example,  a  current  of  11  amperes  is  steadily  flowing 
through  an  arc  5mm.  long,  formed  with  solid  carbons,  llmm. 
and  9mm.  in  diameter,  the  P.D.  between  them  is  55  volts.  It 
might,  therefore,  be  imagined  that  this  current  could  be  sent 
through  such  an  arc  with  a  dynamo  compounded  and  run  at 
such  a  speed  as  to  maintain  exactly  55  volts  between  the 
carbons  with  no  resistance  inserted  between  the  dynamo  and 
the  carbons.  Or  it  might  be  thought  that  this  steady  current 
of  11  amperes  could  be  sent  through  this  arc  by  means  of,  say, 
29  accumulators,  when  such  a  small  resistance  was  inserted  in 
the  circuit  that,  with  a  current  of  11  amperes,  the  accumulators 
maintained  a  P.D.  of  55  volts  between  the  carbons. 


MINIMUM  EXTERNAL  RESISTANCE.  251 

But  when  I  tried  this,  and  similar  experiments  of  keeping 
the  P.D.  between  the  carbons  constant,  the  arc  always  either 
went  out,  or  the  magnetic  cut-out,  set  to  open  at  30  amperes, 
broke  the  circuit.  The  explanation  of  this  is  now  clear,  for 
what  I  was  really  endeavouring  to  obtain  was  a  silent  arc  with 
a  fairly  small  current,  and  a  small  resistance  in  circuit  external 
to  the  arc  ;  in  other  words,  I  was  trying  to  obtain  the  left-hand 
point  of  intersection  between  the  5mm.  curve  and  the  resistance 
line,  and  this,  as  was  proved  above,  is  impossible.  Indeed,  with 
a  set  of  accumulators  having  an  E.M.F.  of  about  58  volts  and 
a  small  resistance  in  circuit,  the  only  current  that  could  flow 
steadily  through  a  5mm.  arc  between  the  carbons  in  question 
was  a  very  large  one  far  greater  than  30  amperes.  The 
value  of  this  current  would  be  known  if  we  could  find  the 
intersection  of  the  resistance  line  with  the  hissing  part  of  the 
5mrn.  curve,  at  a  point  far  off  the  figure,  to  the  right. 

What  we  find,  then,  is  that,  in  order  that  a  given  current 
may  be  maintained  jloiving  through  a  given  length  of  arc, 
there  must  be  a  minimum  external  resistance  in  the  circuit 
which  determines,  also  the  least  E.M.F.  in  the  generator  that 
would  maintain  such  a  current  flowing  through  such  a  length  of 
arc, 

For  example,  whatever  be  the  nature  of  the  generator,  the 
least  resistance  that  can  be  placed  in  the  circuit  to  send  a  steady 
current  of  11  amperes  through  a  5mm.  arc  is  that  given  by 
the  tangent  to  the  5mm.  curve  at  the  point  corresponding  with 
11  amperes.  And  on  drawing  this  tangent  to  the  5mm.  curve 
in  Fig.  79,  we  find  that  it  corresponds  with  a  resistance 
of  0-64  ohm. 

This  minimum  resistance  determines  the  minimum  E.M.F. 
in  the  generator  for  each  current  and  length  of  arc;  for 
example,  on  continuing  the  resistance  line  just  referred  to  for 
the  11-ampere  5mm.  arc  we  find  that  it  cuts  the  axis  of  P.D. 
at  62  volts.  Hence  a  resistance  exceeding  0'64  ohm  must  neces- 
sarily be  placed  in  the  circuit,  and  the  E.M.F.  employed  must 
exceed  62  volts,  although  the  arc  requires  a  P.D.  of  only 
55  volts.  Similarly,  although  we  see  from  Fig.  79  that  a 
12-ampere  3mm.  arc  requires  a  P.D.  of  only  a  little  less  than  49 
volts,  the  preceding  reasoning  tells  us  that,  with  the  solid  carbons 
used,  two  such  arcs  could  not  be  run  in  series  off  the  ordinary 


252  THE  ELECTRIC  AEC. 

constant-pressure  100-volt  electric  lighting  mains,  even  if  the 
supply  pressure  were  kept  absolutely  constant  at  100  volts. 
Or  again,  with  the  solid  carbons  I  used,  two  10-ampere  4mm. 
arcs  could  not  be  run  in  series  off  110  volts  constant-pressure 
mains,  although  each  arc  requires  less  than  53  volts.  Further, 
the  minimum  resistance  was  so  great  for  an  arc  of  7mm.  and 
current  of  2 '5  amperes,  with  the  solid  carbons  I  used,  that 
it  made  the  minimum  E.M.F.  required  more  than  half  as  large 
again  as  the  P.D.  used  in  sending  the  current  through  the  arc 
itself,  for  I  have  calculated  that  the  minimum  E.M.F.  was 
about  139  volts,  while  the  P.D.  needed  by  the  arc  was  only  86 
volts,  as  has  been  mentioned. 

It  may  be  seen  from  Fig.  79  that  the  compulsory  minimum 
resistance  outside  the  arc  is  greater — 

(1)  the  greater  the  length  of  the  arc, 

(2)  the  smaller  the  current. 

But  the  apparent  resistance  of  the  arc  also  increases  with  the 
length  of  the  arc,  and  is  greater  the  smaller  the  current,  so 
that  we  arrive  at  this  very  curious  fact :  When  a  silent  arc  is 
being  maintained  the  smallest  resistance  that  it  is  possible  to  have 
in  the  circuit  external  to  the  arc  is  greater  the  greater  the  apparent 
resistance  of  the  arc,  or,  in  other  words,  the  more  resistance  you 
have  in  the  arc,  the  more  you  need  outside  it. 

Many  more  facts  concerning  the  relations  between  the  E.M.F. 
of  the  generator,  the  external  resistance,  the  length  of  the  arc, 
and  the  current  can  be  ascertained  by  treating  Fig.  79 
analytically,  which  we  will  now  proceed  to  do. 

Let  E  be  the  E.M.F.  of  a  generator  in  volts,  let  r  be  the  total 
resistance  in  ohms  in  the  circuit  outside  of  the  arc  itself,  let 
there  be  a  P.D.  of  V  volts  between  the  carbons,  and  let  a  current 
of  A  amperes  be  flowing  through  an  arc  of  I  millimetres.  Then, 
referring  to  Fig.  79  (p.  242),  E  is  represented  by  the  distance 
between  P  and  the  axis  of  current,  r  by  the  ratio  of  the  distance 
from  P  Q  of  any  point  on  one  of  the  resistance  lines  to  its  distance 
from  the  axis  of  P.D.  This  is  the  same  thing,  of  course,  as  r 
being  represented  by  the  tangent  of  the  angle  between  a 
resistance  line  and  PQ.  A  is  represented  by  the  distance 
between  any  point  at  which  a  resistance  line  cuts  a  curve  and 


CURVES  TAKEN  ANALYTICALLY.  253 

the  axis  of  P.D.  and  V  by  the  distance  between  that  point  and 

the  axis  of  current. 

Then  E  =  V  +  A  r. 

But  from  equation  (4)  (p.  186), 


therefore  E  =  a  +  6/  +       —  +  Ar,      ....    (10) 

A 

or  A2  r  -  (E  -  a  -  b  1)  A  +  c  +  d  I  =  0  ; 


hence       A  =     -- -  a- 6Q'- 4r  (  (u) 

2*  T 

Thus  we  find,  as  before,  that  with  a  generator  of  given  E.M.F. 
two  different  currents,  or  one,  or  none  may  be  sent  through  the 
arc.  The  conditions  for  the  three  cases  in  the  equation  are 
that  (E-a-6/)2  shall  be  greater  than,  equal  to,  or  less  than 
4  r  (c  +  d  /),  and  these  correspond  with  the  conditions  in  the 
figure  that  the  resistance  line  shall  meet  the  curve  at  two 
points,  at  one,  or  not  at  all. 

Since  the  value  for  A  obtained  by  using  the  positive  root  in 
equation  (11)  is  greater  for  any  given  length  of  arc  than  that 
obtained  by  using  the  corresponding  negative  root,  it  follows 
that  the  positive  root  will  give  values  which  correspond  with 
right-hand  points  of  intersection  between  the  resistance  line 
and  the  curve,  while  the  negative  root  will  give  values  that 
correspond  with  the  left-hand  points  of  intersection.  As  it 
has  already  been  shown  that  these  left-hand  points  can  never 
be  obtained  in  practice,  it  will  not  be  necessary  here  to  discuss 
the  negative  root  of  the  equation,  and  therefore  henceforward 
when  equation  (11)  is  mentioned  it  will  be  understood  that  the 
positive  root  only  is  alluded  to. 

As  before,  we  shall  take  a  given  E.M.F.  in  the  generator,  and 
we  shall  consider  what  happens,  first,  when  r  is  constant  and  I  is 
varied ;  next,  when  I  is  constant  and  r  is  varied  ;  and  finally,  when 
r  and  I  are  both  varied  in  such  a  way  that  A  is  constant.  In 
equation  (11),  if  A  is  to  have  a  real  value  at  all,  (E-a-5  I)2 
must  be  not  less  than  4  r  (c  +  d  1)  whatever  A,  E,  r,  and  I  may 
be.  Taking  the  first  case — r  constant,  i.e.t  following  one  of  the 
resistance  lines  in  Fig.  79 — with  the  positive  sign  before  the 


254  THE  ELECTRIC  ARC. 

root,  A  is  evidently  greatest  when  I  is  least,  diminishes  as 
increases,  and  is  least  when  I  is  greatest  —  that  is,  A  is  a 
maximum  when  I  is  a  minimum,  and  a  minimum  when  I  is  a 
maximum  if  the  resistance  external  to  the  arc  is  kept  constant 
But,  since  the  expression  under  the  root  cannot  be  negative 
if  A  is  to  be  real,  I  is  a  maximum  when 

(E-a-&/)2-4r(c  +  d/)  =  0,    .     .     .     (12) 

for,  since  E  is  constant,  E  -  a  -  bl  is  smallest  when  I  is  greatest, 
and  since  r  is  constant,  r  (c  +  d  I)  is  greatest  when  I  is  greatest. 
Hence  when  r  is  constant  the  condition  that  A  shall  have  only 
one  value,  which  is  the  condition  that  the  resistance  line  shall 
be  a  tangent  to  the  curve,  is  also  the  condition  that  the  length 
of  the  arc  shall  be  a  maximum,  as  was  shown  when  the  subject 
was  dealt  with  graphically. 

Since  A  has  been  shown  to  be  a  minimum  when  I  is  a 
maximum,  it  follows  that  the  smallest  current  that  can  flow 
with  a  constant  resistance  in  circuit  when  the  E.M.F.  of  the 
generator  is  also  constant  is  given  by  the  equation 


These  maximum  and  minimum  values  for  I  and  A  may  be 
found  in  terms  of  E,  r,  a,  6,  c,  and  d,  all  of  which  are  known. 
For  from  equation  (12)  we  have 


hence 

7  =  5(E  ~  a)  +  2c*  r  ±  N/{fr(E  -  a)  +  2  dr}*-  62  {(E  -  a)2  - 


or    /_ 


b  b2 

But  from  equation   (11)  it  may  be  seen  that  I  cannot  be 

TG^ 

greater  than  —  I  —  when  the  quantity  under  the  root  is  zero, 

otherwise  A  would  be  negative.     Therefore,  in   the  last  equa- 
tion the  negative  sign  must  be  used  before  the  root. 
The  quantity  under  the  root  is 

&2  (E  -  a)2  +  4  bdr  (E  -  a)  +  4  d2  r2  -  62  (E  -  a)2  +  4  62  c  r, 
which  equals 


CONSTANT  E.M.F.  &  EXTERNAL  RESISTANCE.    255 
Therefore 


And,  substituting  this  value  for  I  in  equation  (13)  we  get 

A=  Jr{bd(&-a)  +  <t'2r  +  b2c}_d 
br  b 

Hence,  if  the  E.M.F.  of  the  generator  be  known,  and  also 
the  external  resistance  that  it  is  desired  to  have  in  the  circuit,  the 
longest  silent  arc  that  can  be  maintained  and  the  smallest  current 
that  will  flow  can  be  found  in  terms  of  the  known  E.M.F.,  the 
known  resistance,  and  the  known  constants  depending  on  the 
carbons  used. 

For  instance,  let  us  take 

E  =  48-88  volts, 
r=   0*5  ohm. 

Then,  from  the  above  equations  we  get 
Z  =  l-35mm, 

and  A  =  7'2  amperes  if  the  values  of  the  constants  are  those 
given  in  equation  (3)  (p.  184). 

Thus,  with  an  E.M.F.  of  48'88  volts  in  the  generator,  and  a 
resistance  of  0'5  ohm  in  the  circuit  external  to  the  arc,  the 
longest  silent  arc  that  can  be  maintained  with  the  carbons  in 
question  is  one  of  l'35mm.,  and  the  smallest  current  that  will 
flow  is  one  of  7'2  amperes. 

Next  let  I  be  constant  and  r  variable,  that  is,  let  us  follow 
the  course  of  one  of  the  curves  for  constant  length  of  arc  in 
Fig.  79.  Then,  of  course,  A  will  also  vary,  and  will  again  be  a 
minimum  when  equation  (12)  holds.  Also  r  will  be  a 
maximum  when  equation  (12)  holds,  since  any  value  of  r 

greater  than  ^  _  ~a~  _  )_  would  make  the  quantity  under  the 
4:(c  +  dl) 

root  in  equation  (11)  negative.  Hence  we  have  for  A  a  minimum 


and  for  r  a  maximum 

_( 


256  THE  ELECTRIC  ARC. 

By  combining  these  two  equations  we  can  obtain  the  following 
one  for  A  in  terms  of  known  quantities  only,  r  being  already 
given  in  known  terms, 


E-a-bl 

Thus,  ivhen  the  E.M.F.  of  the  generator  is  known,  and  it  is 
required  to  maintain  a  silent  arc  of  fixed  length,  the  maximum 
external  resistance  that  can  be  used,  and  the  minimum  current 
that  can  be  maintained,  can  be  found  in  terms  of  the  knoivn 
E.M.F.,  the  fixed  length  of  arc,  and  the  known  constants  of  the 
carbons. 

For  example,  let 

E  =  58-88  volts, 


Then,  from  the  above  equations  we  have 

r=  I'l  ohms, 

and  A  =  6-28  amperes. 

Hence,  with  an  E.M.F.  of  58  -88  volts  in  the  generator,  and 
a  silent  arc  of  3mm.  to  be  maintained,  a  resistance  of  I'l  ohms 
is  the  greatest  that  can  be  placed  in  the  circuit  outside  the  arc, 
and  6  '28  amperes  is  the  smallest  current  that  will  flow. 

Lastly,  let  r  and  I  be  both  varied  in  such  a  way  that  A 
remains  constant,  that  is,  let  us  follow  some  such  line  as 
S  R!  R2  R3  in  Fig.  79.  Then,  from  the  equation 


2A 

it  is  plain  that  r  diminishes  as  I  increases,  and   becomes  a 
minimum  when 

E-a-62 


2A 
—  that  is,  when  the  quantity  under  the  root  vanishes  —  or 


which  has  also  been  found  above  to  be  the  condition  that  I 
shall  be  a  maximum  for  a  fixed  value  of  r, 


CONSTANT  EM.F.  AND  CURRENT.  257 

By  combining  the  last  two  equations  we  can  determine  the 
minimum  value  for  r  and  the  maximum  value  for  I  in  terms  of 
the  known  quantities,  when  E  and  A  are  constant, 


Thus,  when  the  E.M.F.  of  the  generator  is  known  and  the 
current  is  fixed,  the  minimum  external  resistance  that  must  be 
placed  in  circuit,  and  the  maximum  length  of  silent  arc  that  can 
be  maintained,  can  be  found  in  terms  of  the  known  E.M.F.,  the 
fixed  current,  and  the  known  constants  of  the  carbons. 

For  example,  let  us  take 

E  =  58-88  volts, 
A  =  10  amperes. 

Then  from  the  above  equations  we  get 

r  =  0'56  ohm, 
and  Z  =  4'2mm., 

which  shows  that  if  with  an  E.M.F.  of  58-88  volts  in  the 
generator  we  wish  a  current  of  10  amperes  to  flow,  the  smallest 
resistance  that  can  be  placed  in  the  circuit  outside  of  the  arc  is 
one  of  0-56  ohm,  and  the  longest  arc  that  can  be  maintained  is 
one  of  4-2mm. 


SUMMARY. 

I.  With  a  given  E.M.F.  in   the   generator,   and   a   given 
resistance  in  the  circuit  outside  the  arc,  no  arc  longer  than  a 
certain  maximum  length  can  be  maintained,  and  with   this 
length  the  P.D.  between  the  carbons  is  the  greatest,  and  the 
current  flowing  the  least  that  can  be  maintained,  by  the  given 
E.M.F. 

II.  For  the  maintenance  of  each  current  and  length  of  arc  a 
certain  minimum  resistance  is  needed  in  the  circuit  outside  the 
arc,  and  this  resistance  determines  the  value  of  the  smallest 
E.M.F.  with  which  the  generator  could  maintain  the  arc  of  the 
given  length  and  with  the  given  current  flowing. 


258  THE  ELECTRIC  ARC. 

III.  This  minimum   resistance  is  greater  the  greater  the 
length  of  the  arc  and  the  smaller  the  current. 

IV.  If  the  E.M.F.  of  the  generator  and  the  external  resist- 
ance  be  fixed,   the  maximum   length  of  arc,  the   minimum 
current   that   can   be   maintained,    and   the   maximum   P.D. 
between  the  carbons,  can  be  found  in  terms  of  that  E.M.F.  and 
resistance,  and  of  the  four  constants  of  the  carbons. 

V.  If  the  E.M.F.  of  the  generator  and  the  length  of  the  arc 
be  fixed,  the  maximum  external  resistance  that  can  be  used, 
and  the  minimum  current  that  will  flow  can  be  found  in  terms 
of  the  given  E.M.F.  and  length  of  arc  and  the  four  constants 
of  the  carbons. 

VI.  When  the  E.M.F.  of  the  generator,  and  the  current 
are  fixed,  the  maximum  external  resistance  that  can  be  used, 
and  the  maximum  length  of  arc  that  can  be  maintained,  can  be 
found  in  terms  of  the  given  E.M.F.  and  current,  and  the  four 
constants  of  the  carbons. 


CHAPTER   IX. 


SOLID   CARBONS. 

THE  RATIO  OP  THE  POWER  EXPENDED  IN  A  SILENT  ARC  TO  THE 
POWER  DEVELOPED  BY  THE  GENERATOR.  —  THE  RESISTANCE 
NEEDED  IN  THE  CIRCUIT  OUTSIDE  THE  ARC. 

The  ratio  of  the  power  expended  in  a  silent  arc  to  the  power 
developed  by  the  generator  is  an  important  factor  in  determining 
the  most  efficient  arrangement  to  use  in  maintaining  an  arc. 
We  are  now  in  a  position  to  determine  when  this  ratio  of  A  V 
to  A  E  will  be  greatest  with  solid  carbons. 

From  equations  (4)  and  (10)  (pp.  186  and  253),  we  have 

,  ,  ,     c  +  dl 

a  +  bl  + 

.     .     .     (14) 


V  A  V 

Hence,  for  any  given  values  of  I  and  A,  —  ,  and  therefore,  -r-^,is 

JtL  A  & 

greatest  or  nearest  to  unity  when  A.r  is  least  ;  but  from  equation 
(11)  it  is  evident  that  Ar  is  least  when 


that  is,  when  equations  (12)  and   (13)  hold.     From  those  two 
equations  we  find  then  that  when  —  is  greatest 


or  r 

A* 

s2 


(15) 


260  THE  ELECTRIC  AEC. 

This  equation  gives  the  value  of  r,  when  —  is  as  large  as 
possible,  for  any  given  value  of  I  and  A.     It  is  still  necessary 

then,  in  order  to  find  absolutely  the  largest  value  of  —  ,  to  find 

Jii 

what  values  of  I  and  A  make  —  greatest.    If  we  substitute  — 

E  A 

for  A  r  in  equation  (14),  and  multiply  numerator  and  denomi- 
nator by  A,  we  get 

V_ 

E      a  + 


y 

from  which  it  is  plain  that,  whatever  A  may  be,  —  is  greatest 

E 

when  c  +  d  HB  least  —  i.e.,  when  I  is  least,  for  if  the  second  c  +  d  I 

in  the  denominator  were  to  vanish  altogether,  —  would  be  unity. 

E 

Thus  the  ratio  of  the  power  expended  in  a  silent  arc  to  the 
power  developed  by  the  generator  is  greatest  when  the  arc  is 
shortest  —  that  is  when  the  length  of  the  arc  is  zero  if  we  preclude 
negative  lengths,  of  the  existence  of  which  we  have  no  proof. 

To  find  what  value  of  A  makes  —  greatest  for  any  given  value 

E 

of  I,  we  may  put  the  last  equation  in  the  form  — 

V=1_  _  c  +  dl  _ 
E 


y 

which  shows  that,  for  any  given  value  of  I,  —  is  greatest  when 

E 

A  is  as  large  as  possible.     But  A  is  as  large  as  possible  for  a 

silent  arc  of  given  length  when  the  arc  is  about  to  hiss,  so  that 

y 
the  value  of  A  when  —  is  greatest  for  any  given  length  of  arc 

E 

must  be  found  from  the  equation  connecting  I  and  A  for  all  the 
points  on  the  hissing  curve  Xj  X2  X3  Fig.  79  (p.  242  ).  Hence 
the  ratio  of  the  power  expended  in  a  silent  arc  to  the  power 
developed  by  the  generator  is  greatest  when  the  arc  is  on  the  point 
of  hissing. 

Since   A   must  be  as  large   as  possible  and  I  as  small  as 

possible   for  —  to   have   its   greatest   value,    it   follows   from 
E 

equation  (15)  that  r  must  be  as  small  as  possible.     Hence  the 


POWER  EXPENDED  IN  ARC.  261 

ratio  of  the  power  expended  in  a  silent  arc  to  the  power  developed 
by  the  generator  is  greatest  when  the  resistance  in  the  circuit 
outside  the  arc  is  as  small  as  possible. 

It  is  still  necessary  to  find  what  value  of  E  makes  —  greatest 

E 

when  A  and  I  are  fixed,  but  this  is  easy,  for  since  V  and  E  are 
independent  of  one  another  evidently  E  must  be  as  small  as 

possible  for  _  to  be  as  large  as  possible,  or  the  ratio  of  the  power 
E 

expended  in  a  silent  arc  to  the  power  developed  by  the  generator 
is  greatest  when  the  EM.F.  of  the  generator  is  the  least  possible. 

Since  the  experiments  upon  which  the  curves  in  Fig.  79  are 
founded,  and  upon  which  the  above  reasoning  is  based,  were 
made  with  arcs  of  not  less  than  1mm.  in  length,  and  with  solid 
carbons,  it  is  impossible  to  be  sure  that  the  laws  which  have 
been  shown  to  apply  to  these  arcs  would  also  be  true  for 
arcs  of  less  than  1mm.  and  with  cored  carbons.  We  can, 
however,  be  quite  sure  of  the  following :  In  silent  arcs  of 
from  1mm.  to  7mm.,  with  solid  carbons,  the  ratio  of  the  power 
expended  in  the  arc  to  the  power  developed  by  the  generator  is 
greatest  when  the  arc  is  shortest,  when  the  current  is  the  largest 
that  does  not  cause  hissing,  and  when  the  resistance  in  the  circuit 
outside  the  arc,  and  consequently  the  E.M.F.  of  the  generator  is  the 
smallest  possible. 

Although  the  conditions  just  obtained  are  absolutely  the 
best  where  power  only  is  concerned,  such  as,  for  instance,  in 
the  case  of  an  electric  furnace,  it  must  not  be  forgotten  that 
with  arcs  used  for  lighting  purposes  the  final  consideration 
must  always  be  the  greatest  ratio  of  the  light  emitted  to  the 
power  evolved  by  the  generator.  This  ratio  as  it  stands  would 
be  very  difficult  to  find,  but  by  combining  the  conditions 
necessary  for  the  ratio  of  the  power  consumed  in  the  arc  to  the 
power  evolved  by  the  generator  to  be  the  greatest  possible, 
with  the  conditions  necessary  to  make  the  ratio  of  the  light 
emitted  by  the  arc  to  the  power  consumed  in  it  as  large  as 
possible,  the  very  best  arrangement  of  the  circuit  for  an  arc 
used  for  lighting  purposes  may  be  obtained.  All  the  develop- 
ments of  the  first  set  of  conditions  will  be  considered  in  the 
present  chapter,  while  the  second  set,  and  the  combination  of 
the  two,  will  be  discussed  in  Chapter  XI. 


262  THE  ELECTRIC  ARC. 


The  equation  to  the   curve  XjXaXa  —  is,  as  will  be  shown 
later  on, 

.      11-66  +  10-541 
-416Z  ' 


which,  put  in  the  general  form,  is 

A  =  5+*    ......     (16) 


where  c  and  d  have  the  values  already  used  and 

e=M7, 
/=  0-416. 

Thus  we  have  the  three  equations  (12),  (13),  and  (16)  connect- 

y 
ing  the  four  variables  I,  A,  E,  and  r,  when  —  is  a  maximum, 

E 

and  hence,  if  circumstances  determine  any  one  of  the  four,  the 
other  three  can  be  found. 

It  would  appear,  from  what  has  gone  before,  as  if  the  length 
of  the  arc  were  the  most  important  variable  to  choose  first  in 
making  any  arrangement  to  maintain  an  arc,  for  we  know 
definitely  that,  if  we  ignore  for  the  moment  the  question  of 
the  light  given  out,  this  should  be  as  small  as  possible. 

The   difference   between    the   greatest   value   of    —  with  one 

E 

length  of  arc  and   its   greatest  value  with   another   is   not, 

however,  very  large.      For  instance,  for  the  carbons  I  used, 

y 
with  an  arc  of  Omm.  the  greatest  value  of  —  would   be  0'97, 

E 

obtained  with  a  current  of  10  amperes,  an  E.M.F.  of  41  volts, 

and  a  P.D.  of  40  volts  between  the  carbons.     With  an  arc  of 

y 
7mm.  the  greatest  value  of  —  would  be  0'94,  obtained  with  a 

E 

current  of  21  amperes,  an  E.M.F.  of  61'4  volts  and  a  P.D.  of 
57  '4  volts  between  the  carbons.  Hence,  although  the  actual 
power  consumed  in  the  shorter  arc  (400  watts)  would  be  less 
than  one-third  of  that  consumed  in  the  longer  (1205  watts), 
yet  the  ratio  of  the  power  expended  in  the  arc  to  the  power 
developed  by  the  generator  would  be  nearly  the  same  —  viz., 
0-97  and  0'94  —  for  the  two  lengths  of  arc  when  the  largest  non- 
hissing  current  was  used  in  each  case. 


GREATEST  EFFICIENCY.  263 

Thus  it  is  plain  that  in  arranging  a  circuit  so  as  to  obtain  the 

y 

greatest  value  of  — ,  the  length  of  the  arc  matters  very  little. 
E 

This  is  a  fact  of  great  importance  in  the  consideration  of  the 
amount  of  light  given  out  by  the  arc,  for,  as  Prof.  Ayrton 
showed  at  Chicago  in  1893,  the  ratio  of  the  light  given  out  by 
the  arc  to  the  power  consumed  in  it  depends  largely  upon  the 
length  of  the  arc,  and  is  a  maximum  when  the  length  of  the 
arc  is  increased  to  a  certain  value.  Hence,  since  the  length 
of  the  arc  is  practically  immaterial  as  far  as  the  ratio  of  the 
power  consumed  to  the  power  developed  by  the  dynamo  is 
concerned,  in  order  to  decide  what  length  of  arc,  current  and 
E.M.F.  should  be  used  to  insure  the  largest  ratio  of  the  light 
emitted  to  the  power  developed  in  the  generator,  it  would 
simply  be  necessary  to  find  what  length  of  arc  gave  the  greatest 
amount  of  light  for  the  energy  consumed  when  the  current 
flowing  was  the  largest  that  did  not  cause  hissing,  and  we  might 
then  find  out  what  resistance  to  place  in  the  circuit,  and  what 
E.M.F.  to  use,  from  equations  (12)  and  (13). 

For  example,  let  us  suppose  that  the  preceding  considera- 
tions have  led  to  an  arc  of  3mm.  being  chosen,  and  that  the 
arc  lamp  is  fitted  with  a  series  regulating  coil,  and  supplied 
with  current  from  a  generator  of  constant  E.M.F.  With 
such  an  arc  a  current  of  about  18  amperes  is  the  largest  that 
can  be  used  without  hissing,  and  from  equations  (12)  and  (13) 
we  find  that  the  generator  should  have  an  E.M.F.  of  about 
50  volts,  and  that  the  total  resistance  in  the  circuit  outside 
the  arc  should  be  about  0*13  ohm. 

The  current  actually  used  must  not,  however,  be  so  large 
that  the  arc  can  have  any  tendency  to  hiss.  Suppose,  therefore, 
a  normal  current  of  15  amperes  is  selected,  and  that  when  it 
falls  to  13  amperes,  and  the  arc  has  increased  in  length  to 
3'2mm.,  the  regulator  begins  to  feed  the  carbons. 

Then,  remembering  that  the  current  that  is  to  flow  is  no 
longer  the  greatest  non-hissing  current,  but  something  less, 
and  that  E  and  r  are  to  be  the  same  whatever  the  current  and 
length  of  arc  may  be,  we  must  put 

A=15 
/=   3 


264  THE  ELECTRIC  ARC. 

and  also  A  =13 

1  =  3-2 
in  the  general  equation 


in  order  to  find  E  and  r.    In  this  way  we  shall  find  that  E  must 
be  55-5  volts  and  r  must  be  0'5  ohm. 
Hence  we  have  V  or  E  -  A  r  =  55-5  -  7'5 

V       48 


and 


E       55-5 

=  0-87. 


Thus  with  these  carbons,  if  a  silent  arc  of  3mm.  be  main- 
tained with  a  current  of  15  amperes  flowing,  the  arrangement 
can  be  made  so  efficient  that  87  per  cent,  of  the  power 
developed  by  the  generator  will  be  used  in  the  arc,  and  only 
13  per  cent,  will  be  wasted  in  the  resistance  outside  the  arc. 
This  total  resistance  external  to  the  arc  includes,  of  course,  the 
resistances  of  the  generator,  the  leads,  and  the  coil  of  the 
regulator,  so  that  it  might  be  practically  impossible  to  make 

it  as  small  as  0*5  ohm,  but  the  greatest  value  of  —  would  in 

E 

that  case  be  obtained  by  making  this  outside  resistance  as  near 
0-5  ohm  as  possible. 

Without,  however,  for  the  moment  considering  the  new 
circumstance  that  this  impossibility  of  using  a  small  enough 
resistance  introduces  into  the  problem,  we  may  sum  up  the 
ideal  conditions  to  be  striven  for  in  an  arc,  in  order  that  the 
ratio  of  the  power  expended  in  the  arc  to  the  power  developed 
by  the  generator  may  be  as  large  as  possible.  They  are  : 

(1)  That  the  arc  should  be  the  shortest  that  will  emit  the 
requisite  amount  of  light. 

(2)  That  the  current  should  be  the  largest  that  will  certainly 
give  a  silent  arc. 

(3)  That  the  E.M.F   of   the    generator   and   the   external 
resistance  should  be  the  smallest  with  which  this  diminished 
current  could  be  sent  through  the  increased  length  of  arc. 

(4)  That  the  regulator  should  start  feeding  the  carbons  for  as 
small  a  diminution  of  current  and  as  small  an  increase  in  the 
length  of  the  arc  as  possible. 


GREATEST  EFFICIENCY.  265 

It  has  been  shown  that  with  silent  arcs,  when  the  length  is 

y 

fixed,  the  conditions  that  —  shall  have  the  greatest  value  are 

E 

given  by  equations  (12),  (13)  and  (16). 

If  we  put  I  =  0  in  these  equations  and  give  the  constants  the 
values  they  have  for  my  carbons  we  get 

E  =  a  +  2e  =  41'22  volts, 

A  =  -  =  9'96  amperes, 

r  =  —  =  0-1175  ohm, 
c 

I.JLH.0-9718. 

E     a  +  2e 

Having  thus  considered  what  happens  when  I  is  fixed,  we 

will  take  each  of  the  other  four  quantities,  E,  A,  r  and  V,  as 

y 
being  fixed  in  turn,  and  consider  under  what  conditions—    will 

be  the  greatest  in  each  case. 

Since  it  will  be  found  that  the  resistance  external  to  the  arc 
must  in  each  case  be  the  smallest  with  which  the  given  condi- 
tions can  be  carried  out,  I  will  point  out  beforehand  that  in 
equation  (11),  which  may  be  put  in  the  form 


2A  ' 

r  will  be  least  for  any  simultaneous  values  of  A  and  I  when 

(E-a-6Z)2  =  4r(c  +  dO 
—  that  is,  when  equations  (12)  and  (13)  hold. 
Now,  first  let  E  be  fixed,  then  since 
V_E-Ar 
E         E 


=    _ 

T1 

-  will  be  greatest  when  A  r  is  least.    But  from  equation  (1  1)  we 
E 


have     2Ar  =  E-a-6Z+  x(E-a-  &Z)2-4r  (c  +  dl), 
therefore,  for  a  fixed  value  of  E,  A  r  is  least  when  b  I  has  its 
largest  value,  and  when  also 


266  THE  ELECTRIC  ARC. 

is  nought.    That  is,  when  E  is  fixed,  Ar  is  least,  and,  therefore, 

—  is  greatest,  when  we  use  the  longest  silent  arc  possible  with 

E 

the  given  E.M.F.  and  select  the  resistance  external  to  the  arc, 

so  that 


The  last  equation,  which  is  (12),  carries  with  it  equation  (13), 
and  from  the  two  we  find  that 

. 

A  = 


—     —  — 

—  a-bl 

From  this  last  equation  it  follows  that  when  E  is  fixed,  and  I 
is  as  great  as  possible,  A  is  also  as  great  as  possible,  or  ~  is 

greatest  with  a  fixed  E.M.F.  when  A  is  the  largest  silent  current 
that  can  be  maintained  flowing  through  the  arc  of  greatest 
length  that  a  generator  with  the  fixed  E.M.F.  can  produce. 

Now  it  was  shown  on  p.  254  that  equations  (12)  and  (13) 
gave  the  conditions  that  the  line  representing  the  resistance 
r  ohms  should  be  a  tangent  to  the  curve  connecting  P.D. 

and  current  for  the  length  of  arc   Imm.     Thus  it  has   been 

y 
shown  that  when  the  E.M.F.  of  the  generator  is  fixed,  —  is  the 

greatest  possible  when  — 

(1)  The  arc  is  the  longest  that  can  be  maintained  with  the 
fixed  E.M.F.  ; 

(2)  The  line  representing  the  resistance  is  a  tangent  to  the 
curve  connecting  P.D.  and  current  for  this  greatest  length  of 
arc,  and  represents,  therefore,  the  smallest  resistance  that  can 
be  used  with  the  fixed  E.M.F.  ; 

(3)  The  current  is  the  largest  silent  current  for  this  greatest 
length  of  arc. 

But,  as  shown  before,  equation  (16)  gives  the  connection 
between  the  largest  silent  current  for  any  length  of  arc  and 
the  length  of  that  arc.  Therefore  we  may  say  that  when  E  is 

fixed,  equations  (12),  (13)  and  (16)  give  the  relations  between 

y 
E,  A,  /  and  r  that  make  —  the  greatest. 

E 

Next  let  A  be  fixed,  and  first  let  us  suppose  that  I  is  fixed 

also.     Then   from  equation  (14)  (p.  259)  we  see  that  for   — 

III 


GREATEST  EFFICIENCY.  267 

to  be  as  large  as  possible  A  r  must  be  as  small  as  possible.    But 
from  equation  (11)  we  have  that 


-  a  -  b  /)2  -  4  r  (c  +  dl). 
Hence,  whatever  the  length  of  the  arc  may  be,  if  A  is  fixed  A  r 
is  least  when  E  is  least,  and  when  also 


TT 

That  is,  Ar  is  least  —  and  therefore  —  is   greatest  —  when  we 

E 

use  the  smallest  E.M.F.  that  will  send  the  fixed  current 
through  the  arc,  and  when  we  select  r,  so  that  equations  (12) 
and  (13)  hold.  But  when  these  equations  hold,  the  line 
representing  the  resistance  is  a  tangent  to  the  curve  con- 
necting P.D.  and  current  for  the  length  of  arc  used.  Hence, 

when  A  is  fixed,  —  is  greatest,  whatever   length  the  arc  may 

XL 

have,  when  we  use  the  smallest  E.M.F.  that  will  send  the  fixed 
current  through  that  length  of  arc,  and  when  the  line  repre- 
senting the  resistance  is  a  tangent  to  the  curve  connecting 
P.D.  and  current  for  that  length  of  arc. 

Next,  while  A  still  remains  fixed,  let  I  vary.     Then,  since  it 

V  Ar 

has  been  shown  that  —  is  greatest,  whenever  —  -  is  least  and 
Jii  Jii 

Y 

that  when  A  is  fixed,  —  -  is  greatest  when  E  is  least,  we  must 

E  ^r 

now  find  what  value  of  Z  makes  -^-  least,  when  E  is  least,  when 

A  is  fixed,  and  when  equations  (12)  and  (13)  hold. 

Since  E  is  to  be  as  small  as  possible,  Ar  also  must  evidently 
be  as  small  as  possible.     But  from  equations  (12)  and  (13)  we 

.        c  +  dl 

have  Ar=  —   —  , 

A 

which,  since  A  is  fixed,  shows  that  c  +  dl  must  be  as  small  as 

possible  for  A  r  to  be  as  small  as  possible.      That  is,  Ar  is 

Y 
least,  and   therefore  —  is  greatest,  when  I  is  the  shortest  arc 

E 

that  can  be  used,  with  due  consideration  for  the  light  to  be 
emitted.  Y 

Thus,  when  A  is  fixed,  we  find  that  the  conditions  for  .=- 
to  be  as  great  as  possible  are  — 

(1)  That  the  arc  shall  be  the  shortest  that  will  emit  the 
requisite  amount  of  light  ; 


268  THE  ELECTRIC  AEG. 

(2)  That  the  E.M.F.  shall  be  the  smallest  that  will  send  the 
fixed  current  through  this  arc  ; 

(3)  That  the  external  resistance  shall  be  such  that  the  line 
representing  it  will  be  a  tangent  to  the  curve  for  this  arc  at 
the  point  where  the  current  is  the  fixed  current,  and  conse- 
quently the  resistance  must  be  the  smallest  with  which  the 
fixed  current  will  flow  through  the  shortest  length  of  arc. 

Next  let  r  be  fixed,  and  first  suppose  I  to  be  fixed  also.  Then, 

A.r 

since  —  must  be  as  small  as  possible,  we  have  from  equation 
E 

(11)  that 

1-^^  +  L  V(E-a-H)2-4r(c  +  c^) 

must  be  as  small  as  possible.     Hence,  since  I  is  fixed,  E  must 
be  as  small  as  possible,  and 


Ar 

must  be  nought  for  -—-  to  be  least.     Thus,  whatever  the  length 
E 

of  the  arc  may  be,  if  r  is  fixed,  -  -  is  least  when  E  is  least,  and 

E 

when  (ti-a-bl)*  =  4:r(c  +  dl) 

—  that  is,  when  E  is  least,  and  when  equations  (12)  and  (13) 
hold. 

Therefore,  whatever  the  length  of  the  arc  may  be  with  which 

—  is  greatest  when  r  is  fixed,  the  E.M.F.  must  be  the  smallest 
.bj 

that  will  maintain  that  length  of  arc  with  the  given  resistance 
in  circuit,  and  the  line  representing  the  resistance  must  be  a 
tangent  to  the  curve  connecting  P.D.  and  current  for  that 
length  of  arc. 

Now  let  the  length  of  the  arc  vary,  the  resistance  still 
remaining  fixed.  Then,  since  equation  (12)  holds,  whatever 
the  length  of  the  arc,  we  get  from  it 


the  positive  sign  only  being  taken,  because  from  equation  (10) 
(p.  253)  it  may  be  seen  that  E  -  a  -  b  I  could  not  be  negative. 
Hence,  since  E  is  to  be  as  small  as  possible  for  the  fixed 
resistance,  I  must  be  as  small  as  it  can  be  consistently  with  its 


GREATEST  EFFICIENCY.  269 

emitting  the  desired  amount  of  light.     Also,  since  — -  has  to 

ht 

be  as  small  as  possible,  and  since  r  is  fixed  and  E  as  small  as 
possible,  A  must  also  be  as  small  as  it  can  be  with  the  given 

resistance  in  circuit. 

y 

Thus,  when  r  is  fixed,  —  is  the  greatest  possible  when, 
E 

(1)  The  arc  is  the  shortest  that  will  give  the  desired  amount 
of  light ; 

(2)  The  current  is  the  smallest  that  will  flow  through  this 
length  of  arc  with  the  given  resistance  in  circuit ; 

(3)  The  E.M.F.  of  the  generator  is  the  smallest  that  will 
maintain  that  current  flowing  through  that  length  of  arc  with 
the  fixed  resistance  in  circuit. 

Lastly,  let  V  be  fixed,  that  is,  let  a  fixed  P.D.  be  maintained 

between  the  ends  of  the  carbons.     Then  —  must  be  greatest 

jii 

when  E  is  least.      But,  since  E  =  V  +  Ar,  and  V  is  fixed,  E 
must  be  least  when  Ar  is  least.     Now,  from  equation  (11) 


-  a  -  b  If  -  4  r(c  +  d  l)t 
it  is  plain  that  A  r  is  least  when  I  is  greatest,  and  when 
(Et-a-bl)z  =  4:r(c+  dl\ 

that  is,  when  I  is  greatest  and  when  equations  (12)  and  (18) 
hold.     From  these  two  equations,  equation  (15)  is  obtained 


showing  that  since  I  is  to  be  as  large  as  possible,  A  must  also 
be  as  large  as  possible  for  Ar  to  be  as  small  as  possible,  or, 
taking  the  form 

c  +  dl 

A2   ' 

since  A  is  to  be  as  large  as  possible,  r  must  evidently  be  the 
smallest  external  resistance  that  can  be  used  with  the  longest 
arc  that  can  be  maintained  having  the  fixed  P.D.  between  the 
carbons.  Thus,  when  the  P.D.  between  the  carbons  is  fixed, 

the  greatest  value  of        will  be  obtained  by  using 
E 

(1)  The  longest  arc  that  can  be  maintained  with  the  fixed 
P.D.  between  the  carbons  ; 


270 


THE  ELECTRIC  ARC. 


(2)  The  largest  silent  current  that  will  flow  with  this  length 
of  arc  ; 

(3)  The   smallest   external   resistance   and   E.M.F.    of   the 
dynamo  with  which  that  length  of  arc  and  current  can  be 
maintained. 

It  will  be  seen  that  some  of  the  conditions  necessary  to 

ensure  the  greatest  value  of  -  change  considerably  according 

jit 

to  which  of  the  conditions  of  the  circuit  are  taken  as  fixed. 
The  E.M.F.  of  the  generator  and  the  resistance  outside  the  arc 
have  always  to  be  as  small  as  possible,  but  the  length  of  the 
arc  and  the  current  have  sometimes  to  be  as  small  as  possible 
and  sometimes  as  large.  Table  XLII.  gives  a  short  resume  of 
these  condition",  each  variable  being  fixed  in  turn. 

Table  XLII. — Conditions  for  —  to  be  Greatest  when  E,  V,  A, 

E 

/  and  r,  are  Fixed  in  Turn. 


E. 

V. 

A. 

I 

r 

Fixed 
Smallest 
Smallest 
Smallest 
Smallest 

Fixed 

Largest 
Largest 
Fixed 
Largest 
Smallest 

Longest 
Longest 
Shortest 
Fixed 
Shortest 

Smallest 
Smallest 
Smallest 
Smallest 
Fixed 

It  will  not  be  out  of  place  to  give  a  few  examples  of  the  use 
that  may  be  made  of  the  foregoing  methods  of  securing  the 

largest  value  of  —  when  one  or  more  of  the  quantities  with 
E 

which  we  have  to  deal  is  fixed  by  circumstances. 

To  take  first  the  case  of  a  constant  E.M.F.,  let  us  consider 
how  to  arrange  two  arcs  in  series  with  a  dynamo  giving  a  con- 
stant E.M.F.  of  110  volts,  so  as  to  make  the  ratio  of  the  power 
expended  in  the  arc  to  the  power  developed  by  the  dynamo — 

that  is  — — as  large  as  possible. 
E 

There  is  a  constant  E.M.F.  of  55  volts  for  each  arc  and  half 
the  resistance  in  circuit  external  to  the  arcs,  therefore  we  must 
make  E  equal  to  55  in  equations  (12),  (13)  and  (16),  to  find 

what  current,  length  of  arc  and  resistance  external  to  the  arc 

Y 
will  make  -  as  large  as  possible. 

E 


GREATEST  EFFICIENCY.  271 


In  this  way  we  find  that  roughly 

A  =  19-6, 
2=4-7, 
r  =  0-16, 
V     E-Ar 


0-94. 


These  are,  of  course,  the  extreme  conditions,  and  if  these  values 
were  actually  used  the  arc  would  be  very  unsteady,  for  not 
only  would  the  line  representing  the  resistance  be  a  tangent  to 
the  curve  connecting  P.D.  and  current,  in  which  case  it  has  been 
shown  that  the  arc  would  be  unstable  (pp.  245-247)  but  the 
current  would  be  the  largest  silent  current  for  the  length  of  arc, 
and,  therefore,  the  arc  would  be  on  the  point  of  hissing.  But, 
although  we  cannot  actually  use  the  current,  length  of  arc, 
and  resistance  found  from  equations  (12),  (13)  and  (16),  yet 
these  will  serve  as  guides  for  the  choice  of  the  actual  values  to 

be  employed,  so  that  —  may  be  as  large  as  it  is  possible  to 
xL 

be  when  the  arc  is  perfectly  steady. 

Let  us  then  take  an  arc  of  2-5mm.  and  a  current  of  14  amperes, 
so  as  to  be  sure  of  being  well  within  the  limits  of  steadiness. 
We  have  now  to  put  E  equal  to  55,  A  equal  to  14,  and  I  equal 
to  2'5  in  equation  (11),  which  is  the  general  equation  connecting 
E,  A,  I  and  r.  For,  as  we  are  not  now  using  the  largest 
current  and  longest  arc  that  can  be  maintained  with  an  E.M.F. 
of  55  volts,  we  cannot  use  equations  (12),  (13)  and  (16). 

Putting  the  above  values  for  E,  A  and  I  in  equation  (11),  we 
find  that  roughly 

r  =  0'6, 

1  =  0-85. 

Hence,  with  a  constant  E.M.F.  of  55  volts,  and  with  the  solid 

y 
carbons  I  employed,  the  largest  value  of  _,  when  the  arc  was 

E 

silent  and  perfectly  steady,  would  be  obtained  by  having  a 
current  of  about  14  amperes,  an  arc  of  about  2'5mm.,  and  a 
resistance  of  about  0*6  ohm  in  the  circuit  external  to  the  arc. 

With  a  dynamo  having  a  constant  E.M.F.  of  110  volts,  two 
such  arcs  could  be  maintained  in  series,  and,  as  each  arc  would 


272  THE  ELECTRIC  A  EC. 

require  a  resistance  of  0'6  ohm  in  the  external  circuit,  the  total 
resistance  in  the  dynamo,  lea  ds  and  regulating  coil  would  have 
to  be  1-2  ohms,  and  the  ratio  of  V  to  E  would  be  the  same  as 
when  one  arc  was  maintained  with  a  constant  E.M.F.  of  55 
volts— viz.,  0-85.  Hence,  with  such  an  arrangement,  85  per 
cent,  of  the  power  developed  by  the  dynamo  would  be  expended 
in  the  arcs. 

Next  let  the  current  be  fixed.  This  will  be  the  case  when 
theie  are  many  arcs  in  series.  We  must  consider  one  of  these 
arcs  with  its  proportion  of  the  E.M.F.  of  the  generator,  and  of 
the  resistance  of  generator  and  leads. 

Let  us  take  a  fixed  current  of  10  amperes,  and  let  us  suppose 
that  the  arcs  are  found  to  give  the  most  light  when  they  are 
3mm.  in  length. 

Then  we  must  put  A  equal  to  10  and  I  equal  to  3  in  equations 

(12)  and  (13)  to  find  what  E.M.F.  and  resistance  to  use,  so 

y 
that  —  may  be  as  large  as  possible.     Doing  this  we  find  that 

JbLi 

roughly  E  =  54  volts, 

r  =  0'43  ohm, 

T=092' 

With  these  values,  however,  as  before,  the  arcs  would  be 
unsteady.  We  must  use  a  greater  E.M.F.  and  a  higher  resis- 
tance to  maintain  a  steady  arc  of  3mm.  with  a  current  of  10 
amperes.  With  an  E.M.F.  of  60  volts  for  each,  the  arcs  would 
certainly  be  steady.  If,  then,  we  put  E  equal  to  60,  A  equal 
to  10,  and  I  equal  to  3  in  equation  (11),  we  shall  find  what  resis- 
tance must  be  used  outside  each  arc,  so  that  a  steady  arc  may 
be  maintained.  In  this  way  we  find 

r  =  l-06, 
and  Z-  =  0-82. 

Thus,  if  a  constant  current  of  10  amperes  were  flowing,  and 
if  the  arcs  were  kept  exactly  3mm.  in  length,  an  E.M.F.  of  about 
60  volts  and  a  resistance  external  to  the  arc  of  about  1  ohm  for  each 
arc  would,  with  solid  carbons  of  the  diameters  I  employed,  make 

—  as  large  as  it  could  be  for  the  arcs  to  be  in  a  perfectly  stable 
condition.  As,  however,  they  would  not  remain  exactly  3mra. 


GREATEST  EFFICIENCY.  273 

in  length,  the  E.M.F.  would  rise  as  the  arc  lengthened,  until 
the  regulator  acted  and  brought  the  carbons  together  again. 
Thus  the  average  E.M.F.  of  the  generator  should  be  60  volts  for 
each  arc,  and  this  would  be  sufficient  to  allow  of  the  arcs  being 
perfectly  stable.  In  that  case  we  have  seen  that  about  82 
per  cent,  of  the  power  developed  by  the  generator  would  be 
consumed  in  the  arcs. 

Next  let  the  arc  be  at  such  a  distance  from  the  dynamo  that 
the  resistance  of  the  leads,  dynamo  and  regulating  coil  cannot 
be  made  less  than  1  ohm,  and  let  us  suppose  that  under  these 
circumstances  an  arc  of  4mm.  gives  the  best  light  with  uncored 
carbons  of  the  size  and  hardness  employed  in  these  experiments. 

Then,  putting  r  equal  to  1  and  I  equal  to  4  in  equations 
(12)  and  (13),  we  find  that 

A  =  7-3  amperes, 
E  =  61-8  volts, 


Iii  this  case  the  current  must  be  increased  to  make  the  arc 
steady,  for  we  must  raise  the  resistance  line  (Fig.  79,  p.  242) 
to  make  it  cut  the  curve  instead  of  touching  it.  Let  us  then  use 
a  current  of  11  amperes.  Then,  putting  A  equal  to  11,  I  equal 
to  4,  and  r  equal  to  1  in  equation  (6),  we  find  that  roughly 

E  =  63  volts 
and  V  =  0-82. 

Hence,  with  a  resistance  of  1  ohm  in  the  circuit  external 
to  the  arc,  an  E.M.F.  of  63  volts  would  maintain  a  steady  arc 
of  4mm.  with  a  current  of  11  amperes  flowing,  and  82  per 
cent,  of  the  power  developed  in  the  generator  would  be 
expended  in  the  arc, 

Lastly,  let  a  constant  P.D.  of  50  volts  be  maintained  between 
the  carbons.  Then  from  equations  (3),  (12),  (13)  and  (16), 
we  find  that 

I  -4 

A=19 

r  =  0'15 

E  =  53. 


274  THE  ELECTRIC  AEC. 

For  perfect  stability  it  will  be  better  to  take 


A=12. 

Then  from  the  equation         E  =  V  +  Ar 

E  =  56. 

Therefore  -I  =  O89. 

s^ 

THE    SMALLEST   RESISTANCE    THAT    CAN    BE    PLACED    OUTSIDE 
A  SILENT  ARC  WITH  GIVEN  CARBONS. 

It  has  been  shown  that  r  is  always  the  least  resistance  that 
can  be  placed  outside  the  arc  for  any  given  current  to  flow 
through  a  given  length  of  silent  arc  when  equations  (12)  and 
(13)  express  the  relations  between  the  variables.  From  these 
equations  we  get  A?r  =  c  +  dl,  which  shows  that  when  I  is  fixed 
and  r  is  the  smallest  resistance  that  can  be  placed  outside  a 
silent  arc  of  linm,  and  when  a  current  of  A  amperes  is  flowing, 
r  varies  inversely  as  A2. 

Hence,  when  the  arc  is  silent  and  its  length  is  fixed,  the  smallest 
external  resistance  that  can  be  used  with  any  current  varies 
inversely  as  the  square  of  that  current. 

From  this  it  follows  that  with  a  fixed  length  of  arc  the 
larger  the  silent  current  the  smaller  is  the  smallest  resistance 
that  must  be  inserted  in  the  external  circuit  when  that  current 
is  flowing.  Consequently  the  smallest  resistance  that  can  be 
used  in  the  external  circuit  at  all,  when  the  arc  is  silent  and  of 
the  given  length,  is  the  smallest  with  which  the  largest  current 
will  flow  silently.  Thus  the  smallest  resistance  that  can  be 
used  outside  a  silent  arc  of  given  length  is  that  which  is  repre- 
sented by  the  line  which  touches  the  curve  connecting  P.D. 
and  current  for  that  length  of  arc  at  the  hissing  point. 

But  the  relation  between  the  length  of  the  arc  and  the  current 
at  the  hissing  point  will  be  shown  later  to  be  given  by  equation 
(16),  and  the  fact  that  the  resistance  line  is  a  tangent  to  the 
curve  is  expressed  by  equations  (12)  and  (13).  Therefore  from 
those  three  equations  we  can  find  the  smallest  external  resistance 
that  can  be  used  with  any  silent  arc  of  fixed  length, 

Not  only  this,  however,  but  we  can  also  find  from  the  same 
three  equations  the  smallest  external  resistance  with  which  a 


GREATEST  EFFICIENCY.  275 

silent  arc  caii  be  maintained  at  all.     For,  from  equations  (12), 
(13)  and  (16),  we  have 


c  +  dl' 


or 


2/2 

Since  the  quantity  under  the  root  cannot  be  negative  if  I  is  to 
have  a  real  value, 

(dr-leff  cannot  be  less  than  4/2(e2-cr), 
or  d*r*-±dref+±e*f*       „       „      „       „     4e2/2-4C/2r, 
or        d2r~4de/+4c/2       „      „      „       „     zero. 

Hence  d*r-±d  ef+  4  cf2  =  0 

gives  the  smallest  value  that  r  can  have,  and  consequently 


gives  the  value  of  the  smallest  resistance  that  can  be  placed  in 
the  circuit  outside  the  arc  in  order  that  a  silent  arc  may  be 
maintained  at  all. 

Since  this  value  of  r  depends  only  on  the  constants  c,  d,  e 
and  /,  it  is  apparent  that  — 

In  order  to  maintain  a,  silent  arc  at  all  the  total  resistance 
external  to  the  arc  cannot  have  less  than  a  certain  minimum 
value,  which  depends  solely  on  the  carbons  employed. 

By  putting  the  numerical  values  for  the  constants  in  the  last 
equation,  it  will  be  found  that,  with  the  carbons  used  in  my 
experiments,  the  smallest  resistance  that  can  be  placed  in  the 
circuit  outside  the  arc,  for  a  silent  arc  to  be  maintained,  is 
one  of  O'lllT  ohms.  Further,  by  substituting  O1117  for  r  in 
equations  (12),  (13)  and  (16),  it  will  be  found  that  with  that 
resistance  in  circuit  the  length  of  the  arc  must  be  0*6mm.,  and 
the  current,  which  will  be  the  largest  that  will  maintain  a  silent 
arc  of  that  length,  will  be  one  of  12  -7  amperes,  while  the  value  of 

-  will  be  0-967. 

E  V 

Equation  (17)  gives  two  values  of  I  that  make  —  a  maximum 

E 

for  each  value  of  r,  but  those  obtained  from  the  negative  root 

T2 


276  THE  ELEGTEIG  AEG. 

are  either  negative  or  so  small  that  practically  very  little  light 
would  escape  if  the  arc  were  maintained  at  those  lengths. 
Therefore  in  practice  only  the  lengths  given  by  the  positive 
root  would  be  used. 


SUMMARY. 

I.  The  ratio  of  the  power  expended  in  a  silent  arc  to  the 
power  developed  by  the  generator  is  greater 

(1)  The  shorter  the  arc  ; 

(2)  The  larger  the  current ; 

(3)  The  more  nearly  the  resistance  outside  the  arc 

and  the  E.M.F.  of  the  generator  approach  to  the 
smallest  with  which  the  arc  can  be  maintained. 

II.  The  influence  on  this  ratio  of  the  first  of  these,  viz.,  the 
length  of  the  arc,  is  very  trifling. 

Taking  each  of  the  variables  in  turn  as  fixed  we  have — 

III.  With  a  fixed  length  of  arc  the  above  ratio  is  greater  the 
larger  the  current  and  the  smaller  the  outside  resistance  and 
E.M.F.  of  the  generator. 

IV.  With  a  fixed  E.M.F.  in  the  generator  the  ratio  is  greater 
the  longer  the  arc,  the  larger  the  current  and  the  smaller  the 
outside  resistance. 

V.  With  a  fixed  current  the  ratio  is  greater  the  shorter  the 
arc   and   the   smaller  the  E.M.F.   of  the  generator   and  the 
external  resistance. 

VI.  With  a  fixed  external  resistance  the  ratio  is  greater  the 
shorter  the  arc,  the  smaller  the  current  and  the  smaller  the 
E.M.F.  of  the  generator. 

VII.  With  a  fixed   P.D.  between  the   carbons  the  ratio  is 
greater  the  longer  the  arc,  the    larger   the  current  and  the 
smaller  the  external  resistance  and  the  E.M.F.  of  the  generator. 

VIII.  The  smallest  resistance  outside  the  arc  that  can  be 
used  with  any  current  varies  inversely  as  the  square  of  that 
current. 

IX.  There  is  a  certain  minimum  resistance  needed  in  the 
circuit  outside  the  arc,  which  depends  only  on  the  nature  of  the 
carbons  employed. 


CHAPTER   X. 


HISSING  ARCS. 

The  sounds  made  by  the  direct  current  arc  are  very  varied, 
and  in  many  cases  depend  upon  causes  too  obscure  to  have  been 
yet  detected.  There  are,  however,  three,  which  accompany 
well-defined  phenomena,  and  which  may,  therefore,  be  easily 
classified.  These  are  : — (1)  The  sort  of  sound  like  a  kettle  just 
about  to  boil,  which  belongs  to  a  long  arc  with  a  small  current, 
but  which  is  not  accompanied  by  a  diminution  of  the  P.D.  (2) 
The  sharp  hiss  of  an  arc  of  any  length  when  the  current  sent 
through  it  is  too  great  for  a  silent  arc  to  be  maintained ;  this, 
which  is  accompanied  by  a  fall  of  P.D.  is  the  hissing  usually 
referred  to  when  hissing  arcs  are  mentioned.  (3)  A  sound 
rather  like  the  wind  blowing  through  a  crack,  which  comes 
just  before  the  hissing  with  big  currents  begins.  It  is  a 
sound  very  difficult  to  maintain,  for  the  arc  has  a  great 
tendency  at  that  particular  stage  to  become  either  hissing  or 
silent ;  it  is  accompanied  by  a  beautiful  intense  pale  green  light 
along  the  edge  of  the  positive  carbon,  or,  rather,  probably 
coming  from  the  crater  itself,  but  seen  just  above  the  edge  of 
the  crater  in  the  image  on  the  screen.  It  was  when  this  con- 
dition was  reached  that  Mr.  Trotter  found  that  the  arc  rotated 
at  a  speed  varying  from  50  to  450  revolutions  per  second,  the 
latter  speed  being  attained  just  before  the  arc  actually  hissed. 
(See  p.  69.) 

There  seems  to  be  some  idea  that  a  "  hissing  arc  "  proper  is 
necessarily  a  short  arc,  an  idea  which  the  curves  in  Figs.  38  and 
41  must  immediately  dispel.  Hissing  may  occur  with  any  length 
of  arc,  if  the  current  be  increased  beyond  what  the  arc  can  bear 
silently.  The  hissing  obtained  with  a  7mm.  arc  and  a  current  of 


278  THE  ELECTEIC  ARC. 

21  amperes,  for  instance,  is  of  exactly  the  same  character  as 
that  obtained  with  a  current  of  some  10  or  11  amperes  when 
the  carbons  are  quite  close  together.  In  both  cases  it  simply 
means  that  the  current  is  too  big  for  the  arc  to  burn  silently 
with  the  particular  length  employed.  What  happens  is  this  : 
If,  with  any  length  of  arc,  the  current  be  made  small  at  first, 
and  then  gradually  increased,  a  point  is  reached  at  which, 
however  slightly  the  outside  resistance  may  be  diminished,  the 
current  will  no  longer  increase  gradually,  it  suddenly  leaps  up 
2  or  3  amperes,  the  P.D.  as  suddenly  drops  about  10  volts, 
and  the  arc  begins  to  hiss. 

The  part  in  the  curves  marked  "  Hissing  Unstable  State  "  in 
Fig.  41  really  indicates  a  condition  of  the  arc  such  that,  with 
the  given  conditions  in  the  circuit,  no  current  between  the 
highest  for  the  silent  arc  and  the  lowest  for  the  hissing  could 
be  sent  through  the  arc  at  all.  For  instance,  consider  the  curve 
for  a  3mm.  arc.  It  is  there  indicated  that  no  current  between 
17 '5  and  21  amperes  would  pass  through  the  arc.  If,  when  a 
current  of  17*5  amperes  was  flowing,  the  resistance  in  the 
circuit  was  lowered  by  ever  so  little,  the  current  immediately 
leaped  up  to  21  amperes  or  thereabout,  and  the  P.D.  fell  from 
about  46  volts  to  about  37 '5  volts,  and,  however  cautiously 
and  slowly  the  resistance  was  diminished  or  increased,  the  same 
result  followed,  there  would  be  either  a  silent  arc  with  about 
17  J  amperes,  or  a  hissing  arc  with  about  21  amperes. 

It  follows,  then,  that  the  smallest  current  with  which  con- 
tinuous hissing  first  takes  place,  and  the  largest  current  with 
which  a  silent  arc  of  given  length  can  be  maintained  con- 
tinuously are  almost  impossible  to  determine  with  absolute 
certainty.  Within  the  unstable  part  of  the  curve,  before  even 
arriving  at  the  currents  which  simply  refuse  to  go  through  the 
arc  at  all,  one  gets  currents  which  act  in  a  very  exasperating 
manner.  They  will  flow  silently  for  several  minutes,  and  when 
you  think  the  carbons  are  just  formed  for  that  current  and 
length  of  arc,  down  goes  the  pressure,  up  goes  the  current,  and 
the  arc  begins  to  hiss. 

And,  vice  versa,  when  the  arc  is  apparently  hissing  quite 
steadily,  it  will  suddenly  become  silent  with  a  reversal  of  the 
action  of  pressure  and  current ;  and,  of  course,  when  once 
either  of  these  changes  has  really  set  in,  you  have  to  change 


LAWS   OF  HISSING.  279 

the  outside  resistance  to  bring  the  arc  back  to  the  state  you 
require,  and  wait  while  the  carbons  form  again. 

In  Fig.  80,  which  is  a  copy  of  Fig.  38  with  a  few  additions, 
all  the  lines  to  the  left  of  the  curve  ABC  represent  silent 
arcs,  while  immediately  to  the  right  of  this  curve  are  the 
dotted  lines  denoting  the  unstable  condition,  and  still  further 
to  the  right  are  the  lines  representing  the  hissing  arc. 

It  is  important  to  bear  in  mind,  for  reasons  which  will  appear 
later,  that  these  curves  all  represent  normal  arcs. 

Any  discussion  of  the  hissing  arc  must  necessarily  deal  with 
ifc  in  its  three  states:  (1)  when  on  the  point  of  hissing,  (2)  when 
in  the  unstable  condition,  and  (3)  when  actually  hissing. 
Hence,  in  the  present  chapter,  our  attention  will  be  entirely 
directed  to  that  part  of  Fig.  80  that  is  to  the  right  of  the  line 
representing,  say,  12  amperes ;  for  that  part  includes  all  three 
states  for  each  of  the  constant  lengths. 

An  examination  of  these  curves  shows  that  with  the  carbons 
used,  and  with  the  normal  arc,  the  following  results  are  met 
with : — 

(1)  When  the  length  of  the  arc  is  constant  and  the  arc  is 
silent,   it   may  be  made  to    hiss   by  increasing   the   current 
sufficiently. 

(2)  The  largest  current  that  will  maintain  a  silent  arc  is 
greater  the  longer  the  arc. 

(3)  The  hissing  point  always  occurs  on  the  flat  part  of  the 
curve ;  that  is  to  say,  the  P.D.  has  always  gained  a  value, 
which  changes  very   slightly   with  change  of  current  before 
hissing  begins. 

(4)  When  the  current  is  constant   and  the  arc   is   silent, 
shortening  the  arc  will  make  it  hiss. 

(5)  When  the  arc  begins  to  hiss,  the  P.D.  suddenly  falls 
about  10  volts  and  the  current  suddenly  rises  2  or  3  amperes. 

(6)  For  the  hissing  arc  the  P.D.  is  constant   for   a  given 
length  of  arc,  whatever  the  current. 

It  was  Niaudet,*  who,  in  1881,  first  observed  the  fall  of 
about  10  volts  in  the  P.D.  between  the  carbons  at  the  moment 
hissing  began,  and  in  1886  Messrs.  Cross  and  Shepardf  made 

*  La  Lumiere  Electrique,  1881,  Vol.  III.,  p.  287. 

t  Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  1886. 
p.  227, 


280 


THE  ELECTRIC)  ARC. 


REGION  OF  INSTABILITY.  281 

some  very  careful  experiments  to  see  whether  Edlund's  resist- 
ance law  applied  to  hissing  as  well  as  to  silent  arcs.     They 
found  that  it  did,  and  that 
if  r  be  the  apparent  resistance  of  the  arc  in  ohms, 

I  its  length  in  millimetres 

and       a  and  6  constants  for  given  carbons,  depending  on  the 
current  alone,  the  equation 


applies  to  the  hissing  no  less  than  to  the  silent  arc,  a  being 
smaller  however  and  b  greater  with  the  first  than  with  the  second. 

As  far  back  as  1889,  also,  Luggin*  showed  that,  however 
long  an  arc  might  be,  it  would  still  hiss  were  the  current 
increased  sufficiently. 

At  the  Congress  at  Chicago  in  1893,  Prof.  Ayrtonf  first 
drew  attention  to  the  region  of  instability,  or  rather,  the  region 
of  blankness  corresponding  with  the  impossibity  of  maintaining 
any  normal  arc  with  a  particular  range  of  current  for  each 
length.  At  the  same  time  he  pointed  out  in  Fig.  41,  shown  at 
Chicago,  that  whether  the  P.D.  was  descending  as  the  current 
increased  for,  say,  a  4mm.  arc,  or  was  ascending  for,  say,  a 
O'Smm.  arc,  it  became  quite  constant  for  wide  variations  of 
current  with  a  hissing  arc. 

Lastly,  by  a  comparison  of  Fig.  41  with  Fig.  39  he  brought 
out  the  fact  that  the  largest  current  that  would  flow  silently 
with  any  given  length  of  arc  was  increased  by  using  thicker 
carbons.  For  the  carbons  in  Fig.  39  have  about  twice  the 
diameter  of  those  in  Fig.  41,  and  while  the  largest  silent 
current  for,  say,  the  2mm.  arc  in  Fig.  41  is  15-5  amperes,  that 
for  the  same  length  of  arc  in  Fig.  39  is  about  49  amperes,  or 
more  than  three  times  as  great. 

It  is  plain  that  the  dotted  lines  in  Figs.  80,  39  and  41, 
divide  the  curves  into  two  perfectly  separate  parts,  governed 
by  different  laws.  For  to  the  left  of  the  dotted  part  the 
lines  are  all  curved,  and  curved  differently  according  as  solid 
or  cored  positive  carbons  are  used,  showing  that  with  silent 
arcs  the  P.D.  varies  as  the  current  varies,  and  that  the  law  of 
variation  is  different  with  solid  and  cored  carbons.  To  the 

*   Wien  Sitzungsbcrichtc,  1889,  Vol.  XL  VII.,  p.  118. 
f  The  Electrician,  1895,  Vol.  XXXIV,  pp.  336-7. 


282  THE  ELECTRIC  ARC. 

right,  on  the  other  hand,  the  lines  are  all  straight,  and  more  or 
less  parallel  to  the  axis  of  current,  whether  the  positive  carbon 
is  solid  or  cored,  showing  that  with  hissing  arcs  the  P.D.  is  the 
same  for  a  given  length  of  arc  and  a  given  pair  of  carbons, 
whatever  current  is  flowing,  and  that  this  law  is  true  whether 
the  carbons  be  cored  or  solid.  In  fact,  some  complete  sudden 
break-down  appears  to  occur  when  hissing  begins,  upsetting  all 
the  laws  that  have  governed  the  arc  while  it  was  silent,  and 
bringing  the  behaviour  of  cored  and  solid  carbons  into  accord. 

Thus,  the  subject  of  the  hissing  arc  divides  itself  quite 
naturally  into  two  distinct  portions,  the  one  dealing  with  the 
arc  when  the  break-down  is  imminent,  but  before  it  has 
actually  occurred — dealing,  that  is  to  say,  with  the  points  at 
which  the  current  is  the  largest  that  will  flow  silently — the 
hissing  points  as  I  have  called  them ;  and  the  other  dealing 
with  the  arc  after  the  break-down  has  occurred,  and  when, 
therefore,  the  arc  is  really  hissing. 

An  examination  of  Fig.  80  shows  that  the  hissing  points  lie 
well  on  the  curve  ABC,  the  equation  to  which  has  been 
obtained  in  the  following  way :  The  P.D.  of  each  point  on  the 
curve  was  plotted  as  ordinate,  with  its  corresponding  length 
of  arc  as  abscissa,  and  the  result  was  found  to  be  a  very  fair 
straight  line,  the  equation  to  which  was 

V  =  40-05  +  2-49  I (18) 

which  shows  that  at  the  hissing  points  any  given  increase  in 
the  length  of  the  arc  causes  an  increase  in  the  P.D.  between 
the  carbons  that  is  simply  proportional  to  the  increase  of 
length.  That  is  to  say,  for  every  millimetre  that  is  added 
to  the  length  of  the  arc,  2 -49  volts  is  added  to  the  P.D. 
between  the  carbons  at  the  hissing  point. 

In  Table  XLIII.  a  comparison  is  made  between  the  observed 
P.Ds.  between  the  carbons  at  the  hissing  points  and  the  P.Ds. 
calculated  from  equation  (18).  It  will  be  seen  that  the  greatest 
difference  between  any  two  corresponding  values  is  only  0'6 
volt. 

Equating  the  two  values  of  V  given  by  equations  (18)  and  (3) 
(p.  184),  we  get 

40-05  +  2-49  I  =  38-88  +  2-074  I  +  11'66  +  1Q'54/, 
A_  11-66  + 10-54 1 

A~'  ' 


HISSING  POINTS. 


283 


Table  XLIII. — Observed    Values  of  P.D.    between   Carbons  at 
Hissing  Points,  Values  Calculated  from  Equation  (18),  and 
Differences  betiveen  the  Two. 
Solid  Carbons  :  Positive,  llmm.  ;  negative,  9mm.. 


Length  of 
arc  in 

Observed  P.D. 
between  carbons 

P.D.  between  carbons 
in  volts,  calculated 

Difference 

millimetres. 

in  volts. 

from  equation  (18). 

in  volts. 

1 

42-2 

42-5 

-0-3 

2 

44-5 

45-0 

-0-5 

3 

47-5 

47-5 

0 

4 

49-4 

50-0 

-0-6 

5 

53-0 

52-5 

+  0-5 

6 

55-5 

54-9 

+  0-6 

7 

56-9                              57-4 

-0-5 

This  equation  gives,  with  a  very  fair  degree  of  accuracy,  the 
current  for  each  of  the  points  on  the  curve  ABC  for  the 
different  lengths  of  arc,  as  will  be  seen  from  Table  XLIV.,  which 
gives  the  observed  values  of  the  currents  at  the  hissing  points, 
the  values  calculated  from  equation  (19),  and  the  differences 
between  the  two. 

Table  XLIV. — Observed   Values  of  Currents  at  Hissing  Points, 
Values    Calculated  from    Equation    (19),    and   Differences 
betiveen  the  Tiuo. 
Solid  Carbons  :  Positive,  llmm. ;  negative,  9mm. 


Length  of    j  Observedcurrent 
millimetres,  j        in  amPereS' 


Current  in  amperes, 

calculated 
from  equation  (19\ 


1 

14-06 

13-95 

+0-11 

2 

16-55 

16-37 

+  0-18 

3 

17-54 

17-88 

-0-34 

4 

19-22 

19-02 

+  0-2 

5 

20-0 

19-8 

+  0-2 

6 

20-5 

20-5 

0 

7 

21-0 

20-94 

+  0-06 

Difference 
in  amperes. 


If  we  put  equation  (19)  in  the  form 

?_  M7A-11-66 
10-54-0-416  A' 

it  becomes  obvious  that  when 

10-54-  0-416  A  =  0 


284  THE  ELECTRIC  ARC. 

— that  is,  when  A  =  25 '3  amperes — I  is  infinite,  and  hence,  if  this 
equation  holds  for  all  lengths  of  arc,  and  not  only  for  arcs  of 
from  1mm.  to  7mm.,  there  is  a  maximum  current  with  ivhich  a 
silent  arc  can  be  maintained,  and  any  current  greater  than  this 
will  cause  the  arc  to  hiss,  however  long  it  may  be.  With  the 
carbons  I  used  this  maximum  current  is  evidently  25-3 
amperes. 

Equating  the  two  values  of  I  obtained  from  equations  (18) 
and  (19),  we  get 


v     AKM      2-91A-29-02 
or  V  =  40*05  + 


10-54-0-416  A 

as  the  equation  to  the  curve  ABC  when  the  same  axes  and 
units  are  used  as  for  all  the  other  curves  in  Fig.  80,  p.  280. 

To  turn,  now,  to  the  arc  when  hissing  has  actually  begun. 

In  Figs.  44,  45,  46  and  47  curves  were  given  connecting  P.D. 
with  length  of  silent  arc  for  various  constant  currents  with 
each  of  the  four  pairs  of  carbons.  If,  however,  we  proceed  to 
draw  such  curves  for  hissing  arcs,  then,  in  consequence  of  the 
curve  connecting  P.D.  with  current  for  each  length  of  hissing 
arc  being  practically  a  horizontal  straight  line,  we  obtain  only 
one  curve  connecting  the  P.D.  with  the  length  of  the  arc.  For 
this  curve  is  the  same  for  any  current  which  causes  the  arc  to 
hiss.  In  other  words,  all  the  curves  in  any  one  of  Figs.  44, 
45,  46,  or  47  which  refer  to  silent  arcs  close  up  into  a  single 
curve  for  hissing  arcs.  Thus,  the  law  connecting  the  P.D. 
between  the  carbons  with  the  length  of  the  arc,  when  hissing, 
can  be  found  from  Fig.  80,  by  plotting  the  mean  P.D.  between 
the  carbons  for  each  length  of  arc,  when  hissing,  with  the 
corresponding  lengths  of  arc.  In  this  way  we  get  a  straight 
line,  the  equation  to  which  is 

V  =  29-25  +  2-75 1 (20) 

How  far  equation  (20)  really  sums  up  the  facts  may  be  seen 
from  Table  XLV.,  which  gives  the  mean  value  of  the  observed 
P.D.  between  the  carbons  for  each  length  of  hissing  arc,  the 
P.D.  calculated  from  equation  (20),  and  the  difference  between 
the  two, 


P.Ds.  OF  HISSING  ARCS. 


285 


Table  XLV. — Hissing  Arcs.     Mean  of  Observed  Values  of  P.D. 
between  Carbons,  P.Ds.  calculated  from  Equation  (20)  and 
Differences  between  the  Two. 
Solid  Carbons :  Positive,  llmm. ;  negative,  9mm. 


Length  of  arc  in 
millimetres. 

Mean  P.D.  between 
carbons  in  volts. 

P.D.  calculated  from 
equation  (20). 

Difference 
in  volts. 

1 

32-0 

32-0 

0 

2 

34-4 

34-75 

-0-35 

3 

37-8 

37-5 

+  0-3 

4 

40-0 

40-25 

-0-25 

5 

43-0 

43-0 

0 

6 

46-5 

45-75 

+  0-75 

7 

48-0 

48-5 

-0-5 

Equation  (20)  shows  that,  ivith  the  hissing  as  ivith  the  silent 
arc,  a  straight  line  law  connects  the  P.D.  between  the  carbons  with 
the  length  of  the  arc  when  both  carbons  are  solid. 

There  is,  however,  this  vast  difference  between  the  two  laws  : 
that  for  silent  arcs  the  law  only  holds  for  constant  currents  or 
for  the  currents  at  the  hissing  points,  whereas  for  hissing  arcs 
it  holds  whatever  the  current  may  be.  Thus,  while  for  silent  arcs 
the  constants,  which  correspond  with  the  terms  29'25  and  2'75  in 
equation  (20),  are  constant  only  for  each  separate  current,  and 
change  when  the  current  changes,  with  hissing  arcs  they 
remain  the  same  whatever  the  value  of  the  current  may  be. 
For  instance,  the  equation  equivalent  to  equation  (20)  for  a 
normal  silent  arc  with  a  current  of  4  amperes  may  be  found 
from  equation  (3)  (p.  184)  to  be 

V  =  41-79  +  4-71Z, 
and  with  a  current  of  12  amperes  it  is 


but  with  the  hissing  arc  the  equation  is 


whether  the  current  be  one  of  20  amperes,  or  of  50,  and  whether 
the  arc  be  normal  or  not. 

And  here  I  may  explain  the  reason  for  the  great  importance 
of  distinguishing  between  arcs  that  are  normal  and  those  that 
are  not.  We  have  seen  that,  with  normal  arcs  of  any  given 
length,  hissing  only  starts  when  all  the  silent  arcs  have  been 
used  up,  as  it  were  ;  that  is  to  say,  when  the  current  is  greater 


•^A^y 


286  THE  ELECTRIC  AEG. 

than  it  can  be  with  any  silent  arc  of  the  same  length.  But 
with  a  non-normal  arc  of  2mm.  I  have  been  able  to  produce 
hissing  with  a  current  of  11  amperes,  and  to  have  a  silent  arc 
burning  with  a  current  of  28  amperes,  the  same  carbons  being 
used  in  each  case.  This  apparent  anomaly  will  be  fully 
explained  later,  when  we  go  into  the  causes  that  produce 
hissing. 

In  1889,  Luggin  found,  by  measuring  the  fall  of  potential 
between  each  carbon  and  the  arc,  that  the  principal  part  of 
the  diminution  of  P.D.  caused  by  hissing  took  place  at  the 
junction  of  the  positive  carbon  and  the  arc.  Some  experiments 
of  the  same  sort  made  by  myself  gave  the  same  result.  The 
Carbons  used  were,  as  usual,  solid  Apostle  carbons,  the  positive 
llmm.  and  the  negative  9mm.  in  diameter.  The  third  carbon 
to  place  in  the  arc  was  rather  thick,  2mm.  in  diameter,  but, 
like  the  similar  carbons  mentioned  in  Chapter  VII.,  p.  210,  they 
burnt  well  to  a  point  in  the  arc,  and,  with  the  current  employed 
—  25  amperes  —  thinner  carbons  were  consumed  too  rapidly  for 
good  observations  to  be  made. 

The  P.D.  between  the  positive  carbon  and  the  arc  was  found 
by  placing  the  third  carbon  in  the  arc  as  close  as  possible  to 
the  positive  carbon,  and  measuring  the  P.D.  between  the  two 
with  the  high  resistance  voltmeter  mentioned  in  Chapter  VII. 
This  was  easily  done  when  the  arc  was  hissing,  but  was 
impossible  when  the  largest  silent  current  was  flowing,  for  then 
the  mere  insertion  of  the  third  carbon  was  sufficient  to  make 
the  arc  hiss.  Accordingly,  the  P.D.  between  the  positive 
carbon  and  the  arc  when  the  largest  silent  current  was  flowing 
has  had  to  be  calculated  from  the  formula  (given  in  Chapter 
VII.  p.  222)  for  calculating  that  P.D.  with  any  silent  current, 
viz.  : 


In  Table  XLVI.  two  sets  of  currents  are  dealt  with,  viz.,  the 
largest  silent  current  for  various  lengths  of  arc,  and  a  hissing 
current  of  25  amperes,  and  for  each  of  these  sets  of  currents 
and  lengths  of  arc  two  P.Ds.  are  given,  viz.,  the  P.D.  between 
the  main  carbons  and  the  P.D.  between  the  positive  carbon 
and  the  arc  itself. 


P.Ds.  OF  SILENT  AND  HISSING  ARCS. 


287 


Table    XLVI.— P.D.     between     Carbons,     and     P.I),     between 
Positive  Carbon  and  Arc  with  Largest  Silent  Current  and 
•with  Hissing  Current  of  25  Amperes. 
Solid  Carbons  ;  Positive  llmm.  ;  negative  9mm. 


Length  of 
arc  in 
millimetres. 

(1) 

Largest  silent  current. 

Hissing  current  of  25  amperes. 

P.D.  between 
Carbons  in 
volts. 

(2) 

P.D.  between 
positive  carbon 
and  arc  in  volts 
(calculated). 

(3) 

P.D.  between 
carbons  in 
volts. 

(4) 

P.D.  between 
positive  carbon 
and  arc  in 

volts. 

(5) 

1 

2 
3 
4 
5 
6 

42-2 
44-5 
47-5 
49-4 
53-0 
55-5 

321 
32-2 
32-3 
32-4 
32-5 
32-6 

321 

34-6 
37-0 
40-5 
43-9 
45-9 

24-4 
25-2 
25-7 
25-7 
27-9 
27-2 

Now  in  order  to  compare  the  change  in  the  P.D.  between 
the  main  carbons  caused  by  hissing  with  the  corresponding 
change  in  the  P.D.  between  the  positive  carbon  and  the  arc, 
we  must  subtract  column  (4)  of  Table  XLVI.  from  column 
(2),  and  column  (5)  from  column  (3),  and  compare  the 
differences.  These  differences  are  given  in  Table  XLVII. 

Table  XLVII. — Diminution  of  P.D.   between   Carbons  due   to 
Hissing  compared  ivith  Corresponding  Diminution  of  P.D. 
between  Positive  Carbon  and  Arc. 
Solid  Carbons  :  Positive  llmm. ;  negative  9mm. 


Length  of  arc  in 
millimetres. 
(1) 

Diminution  of  P.D. 
between  carbons  due  to 
hissing. 
(2) 

Diminution  of  P.D. 
between  positive  carbon 
and  arc  due  to  hissing. 
(3) 

1 
2 
3 
4 
5 
6 

10-1 

9-9 
10-5 
8-9 
91 
96 

7-7 
7-0 
6-6 
6-7 
4-6 
5-4 

Thus,  for  the  lengths  of  arc  dealt  with,  hissing  causes  a 
mean  fall  of  about  9'7  volts  in  the  total  P.D.  between  the 
carbons,  and  a  mean  fall  of  about  6*3  volts  in  the  P.D.  between 


288  THE  ELECTRIC  ARC. 

the  positive  carbon  and  the  arc.  Hence  of  the  whole  diminu- 
tion of  the  P.D.  between  the  carbons  caused  by  hissing,  about 
two-thirds  takes  place  apparently  at  the  junction  of  the  positive 
carbon  and  the  arc. 

Further,  my  experiments  showed  that  very  little  of  the 
remainder  of  the  diminution,  if  any,  was  due  to  a  fall  of  the 
P.D.  between  the  arc  and  the  negative  carbon ;  therefore,  this 
remaining  diminution  must  be  attributed  to  a  lowering  of  the 
resistance  of  the  arc  itself.  We  may  sum  up  these  results  as 
follows: — 

Of  the  total  diminution  of  the  P.D.  between  the  carbons  caused 
by  hissing,  about  two-thirds  takes  place  at  the  junction  of  the 
positive  carbon  and  the  arc,  and  the  remaining  third  seems  to  be 
due  to  a  lowering  of  the  resistance  of  the  arc  itself. 

From  equations  (18)  and  (20)  we  can  find  the  law  that  con- 
nects the  change  that  takes  place  in  the  P.D.  between  the 
carbons  when  hissing  begins  with  the  length  of  the  arc.  For 
if  we  call  V  the  P.D.  between  the  carbons  at  the  hissing  point 
with  any  given  length  of  arc  I,  and  V  the  same  P.D.  when 
the  arc  of  the  same  length  is  actually  hissing,  then,  from 
these  equations,  we  get 

V-V-IO-8-0-26J     ....     (21) 

which  shows  that  the  longer  the  arc  the  less  the  P.D.  between 
the  carbons  is  diminished  when  its  condition  changes  from  silence 
to  hissing. 

From  Fig.  80  it  might  be  supposed  that,  given  the  length 
of  the  arc,  the  sudden  increase  of  current  that  occurs  when  the 
arc  starts  hissing  was  as  definite  for  that  length  of  arc  as  the 
diminution  in  the  P.D.  This,  for  a  long  time,  I  imagined  to 
be  the  case,  but,  while  trying  to  find  out  what  law  connected 
the  smallest  hissing  current  for  any  given  length  of  arc  with 
that  length,  I  saw  that  the  value  of  that  current  really 
depended  on  the  circuit  outside  the  arc. 

For  let  E  be  the  E.M.F.  in  volts  of  the  generator,  which  we 
will   assume   to   be  constant  and  inde- 
pendent of  the  current ; 
„       r      „       resistance   in   ohms    of   the  whole   circuit 

outside  the  arc ; 
„       I      ,,       length  of  the  arc  in  millimetres ; 


RISE  OF  CURRENT  WHEN  HISSING  BEGINS.     289 

Let  A  be  the  largest  silent  current  in  amperes  ; 
„   V      „       corresponding   P.D.  between   the   carbons   in 

volts  ; 

„    A'     ,,       smallest  hissing  current  in  amperes  ; 
,,    V     ,,       corresponding  P.D.  in  volts. 

Then  E  =  V  +  Ar, 

and,  since  the  change  in  either  E,  or  r,  or  both,  is  infinitely 
small,  when  the  largest  silent  current  changes  to  the  smallest 
hissing  current 

E  =  V  +  AY, 

A'        A        V-V 

.  .  A  -  A  =  -- 


That  is,  the  sudden  increase  of  current  when  hissing  begins  is 
equal  to  the  sudden  diminution  of  P.D.  divided  by  the  resistance 
of  the  circuit  outside  the  arc. 

A'     E  -  V 


But  for  a  given  hissing  point  V,  V  and  A  are  all  constants  ; 
therefore,  for  such  a  point,  A'  depends  simply  on  the  external 
conditions,  and  may  be  calculated  in  terms  of  A,  V,  V,  and 
either  E,  the  E.M.F.  of  the  generator,  or  r,  the  resistance  in 
the  circuit  outside  the  arc. 

It  is  now  possible  to  see  what  the  dotted  lines  in  Fig.  80 
really  mean.  For  let  B  be  the  hissing  point  for  a  given  length 
of  arc,  and  F  G  the  line  connecting  the  hissing  P.D.  with  the 
current  for  the  same  length  of  arc.  Let  E  be  a  point  on  the 
axis  of  P.D.,  such  that  its  distance  from  the  axis  of  current 
measures  the  E.M.F.  of  the  dynamo  when  the  hissing  point  B 
was  found.  Draw  the  line  EB,  and  continue  it  to  meet  FG 
in  F.  Then  the  distance  of  F  from  the  axis  of  P.D.  measures 
the  smallest  hissing  current  possible  for  the  given  length  of  arc 
with  the  given  E.M.F. 

For,  as  has  already  been  shown  on  page  241,  the  slope  of  the 
line  EB  indicates  the  resistance  in  circuit  outside  the  arc 
when  the  point  B  was  found,  and,  since  this  resistance  remains 
practically  unchanged  when  the  arc  begins  to  hiss,  the  point  at 


290  THE  ELECTRIC  AEG. 

which  the  line  EBF  meets  FG  must  give  the  current  that  will 
flow  when  the  arc  first  begins  to  hiss — that  is,  the  smallest  hissing 
current.  Hence  the  slope  of  the  line  B  F  shows  the  resistance  that 
was  in  circuit  outside  the  arc  when  both  the  points  B  and  F 
were  found,  and  the  point  at  which  the  continuation  of  this  line 
meets  the  axis  of  P.D.  shows  the  E.M.F.  that  the  dynamo  had 
at  the  time. 

Consequently  it  now  appears  that  the  dotted  lines  in  the 
unstable  region  constitute  records  of  the  particular  E.M.F.'s 
the  dynamo  was  made  to  give  and  the  particular  resistances 
that  were  in  the  circuit  outside  the  arc,  on  the  various  days 
when  the  experiments  were  made  with  the  different  lengths  of 
arc  several  years  ago. 

Hence,  when  the  largest  silent  current  changes  to  the  smallest 
hissing  current  for  the  same  length  of  arc,  the  value  of  that 
smallest  hissing  current  depends  only  on  the  E.M.F.  of  the 
generator  or  the  resistance  in  the  outer  circuit,  whichever  is  chosen 
first.  Thus,  it  is  possible,  by  choosing  suitable  E.M.F.'s,  to 
make  the  sudden  smallest  hissing  current  have  any  value  greater 
than  that  of  the  largest  silent  current  for  the  same  length  of 
arc,  and  the  larger  the  E.M.F.  the  more  nearly  equal  will  the 
two  currents  be. 

It  is  evident  from  Fig.  80  that  the  smaller  the  E.M.F.  of 
the  generator,  the  larger  will  be  the  value  of  the  smallest 
hissing  current,  for  the  lower  down  will  E  be  on  the  axis  of 
P.D.,  and  therefore  the  farther  will  the  point  F  be  along  the 
line  F  G.  This  explains  a  circumstance  that  puzzled  me 
greatly  when  it  happened,  but  which  is  now  perfectly  com- 
prehensible. Some  years  ago  I  was  using  accumulators  to  main- 
tain an  arc,  and  in  order  to  be  able  to  keep  the  P.D.  between 
the  carbons  as  constant  as  possible,  for  the  experiment  described 
in  Chapter  V.,  p.  171,  I  was  employing  as  small  a  number  of 
cells  as  possible.  I  was  able  to  have  quite  a  moderate  current 
as  long  as  the  arc  was  silent,  but  as  soon  as  it  began  to  hiss, 
the  current  rushed  up  to  some  huge  value  which  would  inevit- 
ably have  ruined  the  cells,  if  I  had  not  had  a  cut-out  arranged 
to  break  the  circuit.  Why  the  first  hissing  current  should  be 
so  much  greater  than  I  was  accustomed  to  find  it  with  the 
dynamos  I  ordinarily  used,  I  could  not  imagine,  but  the  reason 
is  now  perfectly  obvious.  The  hissing  current  was  so  great 


HISSING   WITH  CORED   CARBONS. 


291 


simply  because  the  E.M.F.  of  the  cells  was  so  small,  and  had 
it  been  possible  to  maintain  a  silent  arc  without  any  resistance 
in  the  outside  circuit  except  that  of  the  cells,  which  is  what  I 
was  trying  to  accomplish,  I  might,  except  for  the  cut-out  coming 
into  operation,  have  had  practically  an  infinite  current  when 
the  arc  began  to  hiss. 

The  change  produced  in  the  law  connecting  the  hissing  P.D. 
with  the  length  of  the  arc,  by  coring  the  positive  carbon,  may 
be  gathered  from  Table  XLVIIL,  which  gives  the  values  of  the 
abscissse  and  ordinates  of  the  curve  connecting  P.D.  with 
length  of  arc  for  all  hissing  currents,  when  the  positive  carbon 
was  9mm.  cored  and  the  negative  8mm.  solid. 

Table    XLVIII. — Hissing   Arcs.      P.D.    between    Carbons    and 

Length  of  Arc  for  Any  Current  that  Causes  Hissing. 
Carbons  :  Positive,  9mm.,  cored  ;  negative,  8mm.  solid. 


Length  of 
arc  in 
millimetres. 

P.D.  between  the 
carbons  in  volts. 

Length  of 
arc  in 
millimetres. 

P.D.  between  the 
carbons  in  volts. 

o-o 

0-5 
1-0 
2'0 

29-8 
321 
34-2 
35-8 

3-0 
4-0 
5-0 

8-0 

37-5 
401 
41-5 
49-2 

On  plotting  these  numbers  we  do  not  obtain  a  straight  line, 
as  with  solid  carbons,  but  a  curve.  Thus,  although,  when  the 
arc  hisses,  the  connection  between  P.D.  and  current  for  a  con- 
stant length  of  arc  follows  the  same  law  whether  the  positive 
carbon  be  cored  or  not,  yet  this  is  not  the  case  with  the 
connection  between  P.D.  and  length  of  arc.  For  this  con- 
nection, which  follows  a  straight  line  law  when  both  carbons 
are  solid,  follows  some  far  more  complicated  law — probably 
depending  on  the  relative  dimensions,  composition  and  hardness 
of  the  core  and  its  case — when  the  positive  carbon  is  cored. 

We  now  pass  from  the  consideration  of  the  electrical 
measurements  of  the  arc  to  the  appearance  of  the  crater,  arc, 
and  carbons. 

Every  alteration  of  the  current  and  of  the  distance  between 
the  carbons  naturally  produces  a  corresponding  modification  of 
all  parts  of  the  arc,  but,  until  the  value  of  the  current  attains 
a  certain  magnitude,  which  depends  only  on  the  length  of  the 

u2 


292  THE  ELECTRIC  AEG. 

arc,  with  a  given  pair  of  carbons,  this  change  is  one  of  degree 
merely,  and  not  of  character.  A  greater  current  simply 
produces  a  larger  crater,  a  larger  arc,  and  longer  points  to  the 
carbons.  When  the  special  current  is  reached,  however,  a 
change,  which  is  no  longer  simply  one  of  degree,  takes  place  in 
the  crater.  Instead  of  presenting  a  uniformly  bright  surface 
to  the  eye,  this  becomes  partly  covered  with  what  appear  to  be 
alternately  bright  and  dark  bands,  sometimes  placed  radially, 
like  the  spokes  of  a  wheel,  sometimes  in  one  or  more  sets  of 
concentric  circles,  moving  round  different  centres  in  opposite 
directions.  The  directions  of  rotation  and  whole  positions  of 
the  images  change  continually,  and  the  motion  grows  faster  and 
faster  as  the  current  is  increased. 

When  the  current  is  so  much  increased  that  the  motion 
becomes  too  fast  for  the  eye  to  detect,  the  arc  begins  to  hum, 
and  then,  as  Mr.  Trotter*  first  showed  in  1894,  it  rotates  at 
from  50  to  450  revolutions  per  second.  These  rapid  revolutions, 
which  the  unaided  eye  is  incapable  of  observing,  he  discovered 
by  the  use  of  a  disc  having  alternate  arms  and  spaces,  and  kept 
in  rapid  rotation.  They  appear  to  begin  just  where  the  slower 
oscillations  and  rotations  described  above  become  too  quick  for 
the  eye  to  see  unaided,  and  end  just  as  the  arc  begins  to  hiss, 
for  he  mentions  that  at  450  revolutions  per  second  the  arc 
breaks  into  a  hiss. 

As  soon  as  hissing  begins  the  whole  appearance  of  the  crater 
changes  again ;  a  sort  of  cloud  seems  to  draw  in  round  a  part 
of  it,  moving  from  the  outer  edge  inwards  as  in  (a)  (Fig.  81), 
and  varying  continually  in  shape  and  position.  Sometimes  but 
one  bright  spot  is  left,  sometimes  several,  but  always  the  surface 
is  divided  into  bright  and  dull  parts,  giving  it  a  mottled  appear- 
ance, as  is  seen  in  each  figure  of  Fig.  81.  After  hissing  has 
continued  for  some  time  the  surface  of  the  crater  is  pitted 
with  holes  separated  from  one  another  by  ridges  as  seen  in  (c) 
Fig.  81.  If,  then,  the  current  be  diminished,  so  that  the  arc 
becomes  silent  again,  the  whole  surface  of  the  crater  grows 
dark  for  an  instant,  (e)  Fig.  81,  then  the  ridges  brighten  as  in 
(/)  Fig.  81,  and  finally  it  becomes  bright  again  all  overt . 

*  Proc.  Roy.  Soc.,  Vol.  LVL,  p.  262. 

t  The  photograph  from  which  Fig.  81  was  made  was  kindly  taken  for 
me  by  Messrs.  Fithian  and  Denny,  assisted  by  Mr.  Fawnthorpe,  students 
at  the  Central  Technical  College. 


(e) 


FIG.  81. — Photographs  of  Arcs  (a)  immediately  after  hissing  has  begun, 
(b)  after  it  has  continued  for  a  very  short  time,  (c)  and  (d)  after  it  has 
continued  longer,  (e)  immediately  after  the  arc  has  become  silent  again, 
(/)  after  it  has  been  silent  for  a  very  short  period. 


APPEARANCE  OF  HISSING  ARC.  293 

The  vaporous  arc  itself  undergoes  fewer  modifications;  it 
preserves  the  ordinary  characteristics  of  the  silent  arc  while 
bands  of  light  and  darkness  hold  possession  of  the  crater,  but, 
when  humming  begins,  a  green  light  is  seen  to  issue  from  the 
crater,  and  with  hissing  this  becomes  enlarged  and  intensified, 
till  the  whole  centre  of  the  purple  core  is  occupied  by  a  bril- 
liant greenish-biue  light,  as  is  indicated  in  Fig.  82.  The 
vapour  also  becomes  apparently  less  transparent,  sometimes 
even  almost  opaque  enough  to  hide  parts  of  the  crater  with  a 
sort  of  violet  mist,  as  was  first  mentioned  by  M.  Blondel  in 
1893.* 

Hissing. 


FIG.  82. — Solid  Carbons  :  Positive,  llmm.  ;  negative,  9mm. 
Length  of  Arc,  l'5mm.     Current,  28'5  amperes. 

The  shape  of  the  arc  now  alters  also.  While  it  is  silent  or 
humming,  no  great  difference  can  be  observed  in  its  form. 
With  solid  carbons  it  is  rounded  or  pear-shaped  according  to 
its  length,  and  has  an  appearance  of  great  stability.  But  aa 
soon  as  hissing  occurs,  the  arc  seems  to  dart  out  suddenly 
from  between  the  carbons,  and  to  become  flattened  out.  In 
Fig.  81  this  flattened  appearance  is  well  marked,  as  it  is  also  in 
Fig.  83  and  in  (d)  Fig.  84;  and,  indeed,  these  figures  show 
that  every  part  of  the  vaporous  arc  itself  is  involved  in  this 

*  The  Electrician,  1893,  Vol.  XXXII.,  p.  170. 


294 


THE  ELECTRIC  AEG. 


flattening — the  purple  core,  the  shadow  round  it,  and  the  green 
aureole.  In  (b)  and  (d)  Fig.  81,  which  were  taken  with 
isochromatic  plates,  the  flattening  has  a  curious  brush-like 
appearance,  especially  near  the  positive  carbon.  The  vertical 
shadowy  lines  in  most  of  these  figures  are  noticeable,  and  want 
accounting  for. 

As  regards  the  carbons  themselves,  the  only  important 
modification  of  the  negative  carbon  that  appears  to  be  due 
to  hissing  is  the  formation  of  the  well-known  "mushroom" 
at  the  end  of  that  carbon  with  a  short  hissing  arc.  This  mush- 
room, of  which  a  good  example  is  seen  in  Fig.  82,  is  well 
named,  not  only  because  of  its  shape,  but  also  because  of  the 

Silent. 


FIG.  83.— Carbons  :  Positive,  9mm.,  cored  ;  negative,  8mm.,  solid. 

Length  of  Arc,  (a)  5mm.,  (b)  8mm. 
Current,  (a)  3'5  amperes,  (1)  34  amperes. 

rapidity  of  its  growth,  which  is  so  great  that  while  it  is  forming 
the  carbons  often  have  to  be  separated,  instead  of  being  brought 
together,  to  keep  the  length  of  the  arc  constant. 

And  now  we  come  to  the  most  important  of  all  the  changes 
that  take  place  when  the  arc  begins  to  hiss,  viz.,  the  alteration 
in  the  shape  of  the  positive  carbon. 

During  the  course  of  his  1889  experiments,  Luggin*  observed 
that  the  arc  hissed  when  the  crater  filled  the  whole  of  the  end 
of  the  positive  carbon.  He  was  thus  the  first  to  call  attention 
to  the  fact  that  there  was  a  direct  connection  between  hissing 

*  Wien  Sitzungsliericlite,  1889,  Vol.  XCVIIL,  p.  1192. 


SHAPE  OF  POSITIVE  CARBON. 


295 


and  the  relation  between  the  area  of  the  crater  and  the  cross 
section  of  the  tip  of  the  positive  carbon.     My  own  observation , 


in  1893  led  to  a  conclusion  somewhat  similar  to  Luggin's,  but 
yet  differing  in  an  important  particular.     It  seemed  to  me  that 


296 


THE  ELECTRIG  ARC. 


with  hissing  arcs  the  crater  always  more  than  covered  the  end 
of  the  positive  carbon — that  it  overflowed,  as  it  were,  along  the 
side. 

How  far  this  is  true  will  be  seen  from  an  examination  of 
Figs.  82,  83,  84  and  85,  which  show  the  shaping  of  the  carbons 
under  various  conditions  with  silent  and  hissing  arcs.  These 
figures  have  all  been  made  from  tracings  of  the  images  of 
actual  normal  arcs,  burning  between  carbons  of  various  sizes. 
Fig.  82  is  the  image  of  a  short  hissing  arc,  for  Fig.  83 
the  diameters  of  the  carbons  were  the  same,  but  the  currents 
and  lengths  of  arc  were  different,  for  Fig.  84  the  carbons 


Silent. 


Hissing. 


(a) 


FIG.  85. — Carbons  :  (a)  Positive,  18mm.,  cored  ;  negative,  15mm.,  solid. 

(6)  Positive,  9mm.,  cored  ;  negative,  8mm.,  solid. 

Length  of  Arc.  5mm.     Current,  25  amperes. 

were  all  of  the  same  size,  and  the  arcs  of  the  same  length,  but 
the  current  had  four  different  values,  while  for  Fig.  85  the 
current  and  the  length  of  the  arc  were  the  same  for  both 
(a)  and  (6),  but  the  diameter  of  one  of  the  positive  carbons  was 
twice  that  of  the  other.  The  figures  were  carefully  chosen  with 
special  reference  to  the  shaping  of  the  positive  carbons ;  for, 
with  normal  arcs,  the  shape  of  the  end  of  a  positive  carbon, 
even  taken  quite  apart  from  that  of  the  negative  carbon  and  of 
the  vaporous  arc  itself,  is  capable  of  revealing  almost  the  whole 
of  the  conditions  under  which  the  arc  was  burning  when  the 


EXTENSION  OF  GRATER  WITH  HISSING.         297 

positive  was  shaped.  It  is  possible,  for  instance,  with  a 
normal  arc,  to  tell,  from  a  mere  drawing  of  the  outline  of 
the  positive  carbon  and  of  its  crater,  whether  the  arc  with 
which  it  was  formed  had  been  open  or  enclosed,  short  or  long, 
silent  or  hissing,  burning  with  a  large  or  with  a  small  current 
for  the  size  of  the  carbon. 

Take,  for  example,  Fig.  83,  and  note  the  difference  in  the 
shape  of  the  positive  carbon  with  a  current  of  3 -5  amperes  as 
in  (a),  and  with  one  of  34  amperes,  as  in  (6).  In  the  first  case 
the  tip  of  the  positive  carbon  is  rounded,  so  that  the  crater  lies 
in  its  smallest  cross-section ;  in  the  second,  the  tip  would  be 
practically  cylindrical  for  some  distance,  but  that  the  crater 
has  burnt  away  a  part  of  the  cylinder,  making  the  tip  look  as 
if  it  had  been  sheared  off  obliquely.  Comparing  now  the  tips 
of  the  positive  carbons  when  the  arc  is  silent  and  when  it  is 
hissing  in  all  the  four  figures,  82,  83,  84,  85,  we  find  the  same 
difference.  With  all  the  silent  arcs  the  tip  is  more  or  less 
rounded,  and  the  crater  lies  in  its  smallest  cross-section,  and 
consequently  is  less  in  area  than  any  but  the  smallest  cross- 
section.  With  all  the  hissing  arcs,  on  the  other  hand,  the  tip  of 
the  positive  carbon  is  practically  cylindrical  for  a  short  distance 
at  least,  or  would  be,  but  that  it  is  sheared  away  by  the  crater  ; 
consequently  the  area  of  the  crater  is  greater  than  the  smallest 
cross-section  of  the  tip,  or  indeed  than  the  cross-section  of  the 
tip  for  some  little  distance  along  its  length. 

We  have  now  arrived  at  the  real,  the  crucial,  distinction 
between  a  silent  and  a  hissing  arc.  When  the  crater  occupies 
the  end  only  of  the  positive  carbon,  the  arc  is  silent ;  when  it 
not  only  covers  the  end,  but  also  extends  up  the  side>  the  arc 
hisses.  Hence,  it  must  be  at  the  hissing  point  when  the  smallest 
increase  in  the  area  of  the  crater  will  make  it  begin  to  cover 
the  side  of  the  positive  carbon,  and  this  can  only  be  when  the 
tip  of  that  carbon  has  very  nearly  the  same  cross-section  for 
some  little  distance  from  its  end — in  other  words,  when  its 
sides  are  nearly  vertical. 

It  is  thus  impossible  to  doubt  that  there  is  some  connection 
between  the  extension  of  the  crater  up  the  side  of  the  positive 
carbon  and  hissing,  although,  so  far,  it  has  not  been  possible 
to  detect  which  was  cause  and  which  was  effect.  We  shall 
presently  see  that  the  extension  of  the  crater  is  the  cause  and 


298  THE  ELECTRIC  ARC. 

hissing  the  effect  ;  that,  in  fact,  hissing  is  produced  by  the  crater 
becoming  too  large  to  occupy  the  end  only  of  the  positive  carbon, 
and  by  its,  therefore,  extending  up  its  side. 

Before  proceeding  to  prove  this,  however,  it  will  be  interest- 
ing to  see  how  the  laws  for  the  largest  silent  currents  with 
normal  arcs,  which  have  been  already  obtained  from  the 
electrical  measurements  on  pages  279-284,  may  be  deduced 
on  the  above  hypothesis  from  Figs.  84  and  85. 

In  Fig.  84  we  have  a  series  of  four  normal  arcs  of  the  same 
length,  burning  between  solid  carboas  of  the  same  diameter, 
but  in  (a)  the  current  is  6  amperes,  in  (b)  12,  in  (c)  20,  and  in 
(d)  30  amperes.  The  roundness  of  the  tip  of  the  positive 
carbon  may  be  measured  by  the  obtuseness  of  the  angle 
ABC  between  its  side  and  end.  In  (a)  the  tip  is  very 
nearly  round,  and  the  area  of  the  crater  is  certainly  less  than 
any  but  its  smallest  cross-section  ;  therefore  the  arc  is  certainly 
silent.  In  (b)  the  tip  is  less  rounded,  but  the  arc  is  still  evidently 
silent;  in  (c)  the  angle  ABC  is  much  more  nearly  a  right 
angle,  and  it  is  plain  that  a  very  small  increase  in  the  area  of 
the  crater  would  cause  it  to  burn  up  the  side  of  the  tip,  there- 
fore the  arc  is  near  the  hissing  point.  In  (d)  the  angle  ABC 
is  practically  a  right  angle,  the  tip  of  the  positive  carbon  is 
cylindrical,  and  the  crater  has  evidently  burnt  partly  up  its 
side,  so  that  the  arc  is  hissing.  Thus,  keeping  the  length 
of  the  arc  constant  and  gradually  increasing,  the  current  must 
gradually  bring  us  to  a  hissing  point. 

Next,  I  have  shown  (pp.  13-17),  that  with,  a  constant 
current,  the  end  of  the  positive  carbon  becomes  rounder, 
and  occupies  a  larger  portion  of  the  entire  cross-section  of  the 
carbon  rod,  the  more  the  carbons  are  separated.  Hence,  the 
longer  the  arc,  the  greater  must  be  the  area  of  the  crater,  and 
consequently  the  greater  must  be  the  current  before  the  crater 
extends  up  the  side  of  the  positive  carbon.  Consequently,  the 
longer  the  arc,  the  greater  is  the  largest  silent  current. 

Thirdly,  it  follows  that  when  the  current  and  the  length  of 
the  arc  have  been  increased  to  such  an  extent  that  the  round, 
tip  of  the  positive  carbon  occupies  the  whole  cross  section 
of  the  carbon  rod  itself,  no  further  increase  in  the  size  of  the 
crater  is  possible,  without  a  part  of  it  extending  up  the  side  of 
the  positive  carbon.  Hence  the  largest  silent  current  for  a 


CA  USE   OF  HISSING.  299' 

positive  carbon  of  a  particular  diameter  cannot  exceed  a 
particular  value,  however  long  the  arc  may  be  made.  Lastly, 
similar  reasoning  used  in  conjunction  with  Fig.  85  tells  us  that 
the  thicker  the  positive  carbon  the  greater  must  be  the  largest 
silent  current  for  a  particular  length  of  arc. 

Consequently,  the  fact  that  hissing  occurs  when  the  crater 
covers  more  than  the  end  surface  of  the  positive  carbon  and 
extends  up  its  side,  combined  with  our  knowledge  of  the  way 
in  which  the  positive  carbon  shapes  itself  in  practice,  is 
sufficient  to  enable  us  to  deduce  all  the  laws  given  on  page  279, 
which  govern  the  largest  current  that  will  flow  silently  with 
the  normal  arc  under  given  conditions. 

It  is  also  now  obvious  why,  when  the  arc  is  not  normal,  it 
may  be  made  to  hiss  with  small  currents  and  will  be  silent  with 
quite  large  ones.  For  suppose,  for  instance,  the  end  of  the 
positive  carbon  were  filed  to  a  long  fine  point,  then  a  very  small 
current  would  make  a  crater  large  enough  to  extend  up  the 
side  of  the  point,  and  produce  a  hissing  arc.  But  if,  on  the 
contrary,  the  end  were  filed  flat,  so  as  to  have  as  large  a  cross 
section,  as  possible,  quite  a  considerable  current  could  flow 
silently,  for  in  that  case  it  would  require  the  current  to  be 
very  great  for  the  crater  to  be  large  enough  to  till  up  the  whole 
of  the  end  of  the  positive  carbon. 

We  come  now  to  the  question,  why  should  the  arc  hiss  when 
the  crater  burns  up  the  side  of  the  positive  carbon — what  is  it 
that  happens  then  that  has  not  happened  previously  ?  In 
pondering  over  this  question,  the  possibility  occurred  to  me 
that  as  long  as  the  crater  occupied  only  the  end  surface  of  the 
positive  carbon  it  might  be  protected  from  direct  contact  with 
the  air  by  the  carbon  vapour  surrounding  it,  but  that,  when 
the  crater  overlapped  the  side,  the  air  could  penetrate  to  it 
immediately,  thus  causing  a  part  at  least  of  its  surface  to  burn 
instead  of  volatilising.  The  crater  would  probably  burn  more 
quickly  than  it  would  volatilise,  and  hence,  though  the 
burning  parts  would  be  at  a  lower  temperature  than  the 
remainder,  and  so  look  duller,  they  would  consume  more 
rapidly,  so  that  little  pits  would  form,  which  would  deepen 
while  the  air  continued  to  get  to  them.  Thus,  the  darker, 
spherical  parts  of  the  crater  shown  in  Fig.  81  (which  you  can 
see  deepen  by  watching  the  image  after  the  arc  has  begun  to- 


300  THE  ELECTRIC  AEC. 

hiss)  would  be  the  burning  parts,  while  the  brighter  ridges 
would  be  volatilising. 

Many  circumstances  at  once  seemed  to  combine  to  show  that 
this  was  the  true  explanation.  The  whirling  figures,  and 
Mr.  Trotter's  still  faster  rotations,  how  were  they  caused  but 
'by  draughts  getting  into  the  arc  ?  Then  the  humming  noise, 
which  is  so  like  the  wind  blowing  through  a  crack,  was  not 
this  probably  caused  by  the  air  rushing  through  a  slight 
'breach  in  the  crater  already  getting  near  to  the  critical  size  ? 
'This  air,  pouring  in  faster  and  faster  as  the  breach  widened, 
would  cause  the  arc  to  rotate  faster  and  faster,  sometimes  in 
one  direction,  sometimes  in  another,  according  as  the  draught 
was  blown  from  one  side  or  the  other.  Then  finally  the  air 
would  actually  reach  the  crater,  burn  in  contact  with  it,  and 
'the  P,D.  would  fall  and  the  arc  would  hiss. 

The  following  is  Mr.  Trotter's  own  explanation  of  the 
rotation  discovered  by  him.  It  is  taken  from  a  letter  on  the 
subject  written  by  him  to  Prof.  Silvanus  Thompson,  about  the 
end  of  June,  1894. 

"The  crater  is  pouring  out  a  stream  of  carbon  vapour. 
With  a  strong  stream  of  vapour  and  a  short  arc,  the  stream 
•may  touch  the  negative ;  when  it  does  so  in  sufficient  volume, 
and  to  exclusion  of  oxygen,  mushrooming  occurs.  But  as  a 
rule  most  of  it,  if  not  practically  all  of  it,  ceases  to  be  carbon 
vapour  before  it  reaches  the  negative.  This,  I  want  to  settle 
by  spectroscope. 

"  There  is  a  combustion  of  the  vapour,  and  that  means  an 
inrush  of  air.  .  .  .  The  inrush  of  air  is  radial.  It  is 
partly  due  to  the  oxygen-carbon  combustion,  partly  also, 
perhaps,  to  the  oxygen-nitrogen  combustion.  If  any  accidental 
cause,  such  as  a  spurt  of  vapour  from  an  impurity  in  the 
carbon,  cause  the  inrush  to  be  otherwise  than  radial,  a  rotatory 
•motion  is  started,  and  persists,  as  when  water  running  from  a 
wash-basin  moves  in  a  vortex.  In  a  washbasin  the  water  can 
get  away,  in  a  tornado  also,  the  air  can  get  upwards  and 
outwards ;  but  in  the  arc  condensation  due  to  chemical  com- 
bination and  lowering  of  pressure  must  be  looked  for  as  a  sink 
for  the  vapour  stream." 

In  the  open  arc,  whether  silent  or  hissing,  the  outer  envelope 
•of  the  vaporous  portion  is  always  bright  green.  With  the 


AIR  THEORY  OF  HISSING.  301 

hissing  arc  the  light  issuing  from  the  crater  is  also  bright  green, 
or  greenish  blue.  What  so  likely  as  that  the  two  green  lights 
should  have  a  common  origin,  viz.,  the  combination  of  carbon 
with  air  ?  For  the  outer  green  light  is  seen  just  at  the  junction 
of  the  carbons  and  carbon  vapour  with  the  air,  and  the  inner 
one  only  appears  when  air  can  get  direct  to  the  crater. 

Again,  why  does  the  arc  always  hiss  when  it  is  first  struck  ? 
Is  it  not  because  a  certain  amount  of  air  must  always  cling 
to  both  carbons  when  they  are  cold,  so  that  when  the  crater 
is  first  made  its  surface  must  combine  with  this  air  ? 

The  cloud  that  draws  in  round  the  crater  when  hissing 
begins  would  be  a  dulness  caused  by  the  burning  part  of  the 
crater  being  cooler  than  the  parts  which  were  still  volatilising. 
In  fact,  everything  seemed  to  point  to  the  direct  contact  of 
crater  and  air  as  being  the  cause  of  the  diminution  in  the 
P.D.  between  the  two  carbons  which  is  the  important  part  of 
the  hissing  phenomenon. 

One  easy  and  obvious  method  of  testing  this  theory  imme- 
diately presented  itself.  If  air  were  the  cause  of  the  hissing 
phenomena,  exclude  the  air  and  there  would  be  no  sudden 
diminution  of  the  P.D.  between  the  carbons,  however  great  a 
current  might  be  used.  Accordingly  I  tried  maintaining  arcs 
of  different  lengths  in  an  enclosed  vessel,  and  increasing  the 
current  up  to  some  40  amperes.  No  sudden  diminution  of  the 
P.D.  could  be  observed  with  any  of  the  currents  or  lengths  of 
arc  employed,  although  when  the  same  carbons  were  used  to 
produce  open  arcs,  the  sudden  diminution  of  about  10  volts  in 
the  P.D.  between  the  carbons  occurred  with  a  current  as  low  as 
14  amperes  for  a  1mm.  arc.  Indeed,  so  far  from  there  being 
any  sudden  diminution  in  the  P.D.  when  the  current  through 
an  enclosed  arc  is  raised  to  higher  and  higher  values,  the  P.D. 
appears  to  increase  slightly  for  large  currents. 

It  was,  of  course,  impossible,  in  these  experiments,  to  avail 
myself  of  an  ordinary  enclosed  arc  lamp,  since  a  current  of 
some  5  or  8  amperes  only  is  all  that  is  used  with  such  a  lamp, 
whereas  to  test  my  theory  it  was  necessary  to  employ  currents 
up  to  40  amperes,  although  my  carbons  were  of  smaller 
diameter  than  those  fitted  in  ordinary  commercial  enclosed  arc 
lamps.  Accordingly,  I  constructed  little  electric  furnaces, 
some  made  out  of  fire-clay  crucibles  with  lids  of  graphite  sealed 


.302 


THE  ELECTRIC  AEG. 


on,  as  in  Fig.  86,  some  moulded  out  of  fire-clay  with  mica  win- 
dows inserted,  so  that  the  image  of  the  arc  could  be  projected 
on  to  a  screen  and  its  length  kept  constant ;  some  constructed 
of  iron  lined  with  asbestos  ;  some  with  tubes  inserted  in  them 
through  which  the  air  could  be  admitted  when  required,  &c. 

It  was  found  that  when  the  vessel  was  entirely  enclosed,  the 
pressure  in  it  was  so  great  when  the  arc  was  first  started,  that 
-occasionally  the  lid  was  blown  off.  Consequently,  the  space 
•between  the  positive  carbon  and  the  lid  was  left  open  till  the 


L'ppor  Carbon 


Ring  of  Sheet  Aibartos 
Aobectos  Fibre 
•Graphite  Lid 


Joint  of  Sodium  Si!icat3 
and  Plaster  of  Paris 


Fireclay  Pot 


-Fireclay  Cement 


"Sodium  Silicate  and 
Plaster  of  Paris  Cement 


"Lower  Carbon 

FIG.  86. 


a-rc  was  well  started,  and  then  was  tightly  closed.  This  sudden 
increase  of  pressure  probably  took  place  when  the  carbons 
were  first  brought  into  contact,  for  Mr.  Seaton,  while  conduct- 
ing some  experiments  for  Messrs.  De  la  Rue  and  Miiller  in  1879 
{p.  38)  observed  that,  when  the  arc  was  completely  enclosed, 
the  increase  of  pressure  when  the  carbons  were  first  brought 
into  contact  was  far  greater  than  could  be  accounted  for  by 
the  rise  of  temperature  of  the  gas  in  the  vessel,  and  that  the 
pressure  fell  the  moment  the  carbons  were  separated,  almost 


ARC  ENCLOSED  IN  CRUCIBLE.  303 

to  what  it  had  been  before  contact  was  made.  This  fact  was 
confirmed  by  some  experiments  made  by  Stenger  (p.  44),  in  1885. 
This  first  great  rise  of  pressure  may,  of  course,  be  partly 
caused  by  the  gases  occluded  in  the  carbons  being  expelled 
on  the  current  being  started,  but  a  complete  investigation 
of  this  phenomenon  has-  not,  as  far  as  I  am  aware,  yet  been 
made. 

Some  curves  connecting  the  P.D.  between  the  carbons  with 
the  current,  when  the  arc  was  completely  enclosed  in  the 
crucible  (Fig.  86)  are  given  in  Fig.  87.  The  carbons  were 
solid,  the  positive  being  llmm.  and  the  negative  9mm.  in 
diameter,  similar  to  those  I  have  used  for  all  my  experiments. 
As  this  crucible — the  first  one  made — had  no  window,  the 
length  of  the  arc  could  not  be  kept  quite  constant,  but  the 
distance  by  which  the  carbons  were  separated  was  noted  at  the 
beginning  of  the  experiment,  and  they  were  then  allowed  to 
burn  away  without  being  moved  till  the  end,  when  the  distance 
the  positive  carbon  had  to  be  moved  in  order  to  bring  it  tightly 
against  the  negative  was  noted.  Measured  in  this  way,  the 
length  of  the  arc  was  l'5mm.  at  the  beginning  and  2mm.  at 
the  end  of  the  experiment.  The  current  was  started  at  6 
amperes,  and  gradually  increased  to  39  amperes ;  then  as 
gradually  diminished  to  6  amperes  again,  increased  to  36 
amperes,  and  diminished  to  5  amperes,  when  the  arc  was 
extinguished.  The  P.D.  between  the  carbons  for  a  given 
current  seems  to  have  increased,  as  the  length  of  time  during 
which  the  arc  had  been  burning  increased ;  this  was 
undoubtedly  partly  due  to  the  lengthening  of  the  arc,  but  was 
probably  also  partly  due  to  the  whole  of  the  air  in  the  pot 
having  been  gradually  burnt  up,  or  driven  out  through  the 
slag  wool  and  the  asbestos  ring,  by  the  pressure  of  the  carbon 
vapour. 

Many  other  sets  of  curves  were  obtained,  but  all  with  the 
same  result,  viz.,  that  when  once  the  crucible  had  been  freed 
from  air,  no  sudden  diminution  in  the  P.D.  could  be  observed  on 
increasing  the  current  far  beyond  the  value  at  which  this 
diminution  took  place  on  lifting  up  the  lid  and  allowing  the 
air  to  have  access  to  the  arc. 

The  next  thing  to  do  was  to  try  if  an  open  arc  could  be  made 
to  hiss,  and  the  P.D.  to  diminish  suddenly,  by  blowing  air  at  the 


304 


THE  ELECTEIC  ABC. 


HISSING  DUE  TO  OXYGEN.  305 

crater  when  the  current  was  so  small  that  the  crater  remained 
well  at  the  end  of  the  positive  carbon — in  fact,  to  bring  the 
air  in  contact  with  the  crater  artificially,  when  a  much  smaller 
current  was  flowing  than  would  usually  produce  hissing.  I 
first  tried  inserting  a  carbon  tube  in  the  arc  and  blowing 
through  it,  but  this  almost  invariably  blew  the  arc  out.  Then 
a  tubular  positive  carbon  was  used  and  the  air  was  blown  down 
it.  This  plan  answered  admirably,  for  when  a  current  of 
10  amperes  was  flowing  with  an  arc  of  about  3mm.,  so  that 
the  arc  was  quite  silent,  each  puff  of  air  blown  down  through 
the  positive  carbon  was  followed  by  a  hiss  and  the  characteristic 
diminution  of  the  P.D.  between  the  carbons.  With  a  current 
of  6  amperes,  however,  I  could  get  no  hiss,  but  simply  blew 
the  arc  out  with  each  puff,  probably  because,  with  such  a  small 
current,  the  arc  was  cooled  sufficiently  to  be  extinguished 
before  the  action  could  take  place. 

Oxygen  was  next  tried,  still  with  the  open  arc,  and  again 
each  puff  produced  a  hiss  and  diminution  of  the  P.D.,  the 
latter  being  exactly  the  same  in  amount  as  when  air  was 
used,  namely,  about  10  volts.  As  my  idea  was  that  the 
diminution  of  P.D.  was  due  to  the  chemical  combination  of  air 
with  carbon  at  the  temperature  of  the  crater,  the  fact  of  oxygen 
causing  the  same  diminution  of  the  P.D.  as  air  seemed  to 
show  that  nitrogen  would  produce  no  effect,  and  that  all  the 
effect  produced  by  air  was  due  to  the  oxygen  in  it.  Accordingly 
nitrogen  was  blown  down  the  positive  carbon  of  an  open  arc, 
and  no  change  in  the  P.D.  followed,  if  the  nitrogen  was  blown 
through  gently ;  but  beyond  a  certain  pressure,  the  arc  was 
blown  to  one  side,  and  thus  lengthened,  so  that  the  P.D.  rose, 
and,  if  the  pressure  continued,  the  arc  went  out. 

This  experiment  proved  two  things — firstly,  that  it  is  the 
oxygen  in  the  air  that  causes  the  diminution  in  the  P.D.  with 
hissing ;  secondly,  that  this  diminution  in  the  P.D.  is  not  due 
to  cooling,  for  nitrogen  would  cool  the  arc  as  effectually  as 
oxygen  or  air. 

To  make  assurance  doubly  sure  on  this  point,  carbon  dioxide 
was  blown  down  the  tubular  positive  carbon,  with  the  same 
result  as  when  nitrogen  was  used,  viz.,  no  change  was  pro- 
duced in  the  P.D.  between  the  carbons  unless  the  pressure 
of  the  gaseous  stream  were  large  enough  to  blow  the  arc  on 


HOC 


THE  ELECTRIC  ARC. 


one  side,  and  then  an  increase  and  not  a  diminution  in  the  P.D. 
was  observed. 

If,  however,  the  current  was  very  near  the  value  that  made 
an  open  arc  of  the  particular  length  used  start  hissing,  blowing 
either  nitrogen  or  carbon  dioxide  through  the  positive  carbon 
sometimes  started  hissing ;  but  this  was  due,  not  to  any  direct 
action  of  the  stream  of  gas  on  the  carbon,  but  to  the  arc  being 
deflected  by  the  gaseous  stream  and  burning  obliquely  up  the 
side  of  the  carbon,  and  thus  allowing  the  air  to  come  into  con- 
tact with  the  crater.  The  proof  of  this  was  that  this  diminution 
in  the  P.D.  had  the  same  value  as  if  air  had  been  employed, 
and  that  the  hissing  did  not  cease  on  stopping  the  stream  of 
nitrogen  or  carbon  dioxide. 

This  was  not  the  case  with  hydrogen,  however.  When  that 
gas  was  blown  down  the  positive  carbon  in  the  open  air,  the  arc 
would  start  hissing  if  the  current  were  large  enough,  and  stop 
hissing  the  moment  the  hydrogen  ivas  shut  of.  Not  only  this, 
but  the  diminution  in  the  P.D.  had  a  different  value  from  that 
produced  by  air,  being  only  about  6'5  volts  instead  of  10  volts. 
Table  XLIX.  gives  the  current  and  the  P.D.  between  the  carbons 
just  before  the  hydrogen  was  turned  on,  just  after  it  was 
turned  on,  just  before  it  was  turned  off,  and  just  after  it  was 
turned  off. 

Table  XLIX. — Effect   of  Blowing   Hydrogen   doivn  a  Tubular 

Positive  Carbon  of  an  Open  Arc. 

Carbons:     Positive,    llmm.,    tubed',    negative,    9mm.,    solid. 
Length  of  arc  about  3mm. 


P.D.  between  carbons  in  volts. 

Current  in 
amperes. 

Before  H  was 
turned  on. 

After  H  was 
turned  on. 

Before  H  was 
turned  off. 

After  H  was 
turned  off. 

52 
52 
52 
52-5 
52 

46 
45 
45 
46 
45 

46 

47 
45 
46 
46 

53 

52 
52-2 
53 
52 

14 
12 
12 
12 
9 

Thus,  the  mean  diminution  of  P.D.  accompanying  the  hissing 
caused  by  hydrogen  being  sent  down  the  positive  carbon  of  an 
arc  burning  in  the  air  was  about  6-6  volts,  or  about  3J  volts 
lower  than  when  the  hissing  was  caused  by  air  alone, 


HISSING   WITH  HYDROGEN.  30 

In  order  to  exclude  all  possibility  of  doubt  as  to  the  effect  of 
the  various  gases,  the  experiments  were  repeated  with  the  arc 
entirely  enclosed,  so  that  the  only  gases  that  could  reach  it 
were  those  blown  down  the  tubular  positive  carbon.  The 
current  was  distinctly  below  the  hissing  point,  being  only  10 
or  11  amperes,  with  an  arc  of  from  2mm.  to  3mm.  long. 

When  air  was  blown  down  the  positive  carbon,  each  puff 
lowered  the  P.D.  by  about  10  volts,  and  the  moment  the 
puff  ceased  the  P.D.  rose  again.  Next,  oxygen  was  tried,  with 
the  same  result.  Thirdly,  nitrogen  with  no  result,  or  with 
the  result  that  the  arc  was  blown  out  if  the  pressure  was 
too  great.  Carbon  dioxide  had  the  same  effect  as  nitrogen, 
and  lastly  hydrogen  was  tried.  This  gas  gave  a  totally 
different  result  with  the  enclosed  arc  from  that  already  obtained 
with  the  open  arc.  For  whereas,  as  has  been  previously  stated, 
hydrogen  produced  a  distinct  hissing  of  its  own  when  blown 
down  the  positive  carbon  in  the  open  air,  it  produced  none  when 
used  in  the  same  way  with  the  enclosed  arc. 

To  prove  that,  in  order  to  produce  the  sudden  diminution  of 
P.D.  under  discussion  it  was  necessary  for  the  active  gas  to 
actually  touch  the  crater,  a  tubular  negative  carbon  was  usedj 
and  each  gas  was  blown  up  through  it  in  turn,  gently  enough 
not  to  force  the  gas  directly  against  the  crater. 

In  no  case  was  there  any  sudden  diminution  of  the  P.D., 
whatever  was  the  gas  blown  through  the  negative  carbon,  and 
whether  the  arc  was  open  or  enclosed.  On  the  contrary,  there 
was  generally  a  small  increase,  probably  due  to  the  lengthening 
of  the  arc  by  its  being  blown  on  one  side.  If  oxygen  or  air 
were  blown  very  hard  up  the  negative  carbon,  they  would  either 
produce  hissing,  or  blow  the  arc  out,  or  both  ;  for  in  that 
case  some  of  the  gas  got  to  the  crater  uncombined  with  the 
carbon  vapour,  and  acted  exactly  as  if  it  had  been  blown  down 
the  tubular  positive  carbon. 

An  interesting  proof  that  the  air  must  be  in  contact  with  the 
crater  to  produce  hissing  is  afforded  by  an  experiment  carried 
out  by  Cravatb,  mentioned  on  page  63.  He  tried  the  effect  of 
moving  one  carbon  horizontally  over  the  other,  while  a  steady 
silent  arc  was  burning.  When  the  positive  carbon  was  pointed 
and  the  negative  flat,  the  arc  burned  silently  as  before,  but 
when  the  negative  carbon  was  pointed  and  the  positive  flat,  each 


308  THE  ELECTRIC  ARC. 

change  of  position    caused    a    hiss.     The    reason  is  obvious. 
Each  change  of  position  caused  a  new  crater  to  form  of  carbon 
that    had    previously    been    in    contact    with    the    air,    and, 
consequently,  still  had  some  air  clinging  to  it. 
The  case,  then,  stands  thus  :— 

(1)  When  the  arc  begins  to  hiss  in  the  ordinary  way,  the 
P.D.  between  the  carbons  diminishes  by  about  10  volts. 

(2)  If  the  air  is  excluded  from  the  arc,  this  diminution  of 
the  P.D.  does  not  take  place,  even  when  the  current  is  nearly 
three  times  as  great  as  would  cause  hissing  in  the  air. 

(3)  If,  however,  while  the  air  is  excluded,  puffs  of  air  are 
sent  against  the  crater,  the  diminution  of  the  P.D.  does  occur, 
even  with  currents  much  smaller  than  would  cause  hissing  in 
the  air. 

(4)  If,  instead  of  air,  oxygen  is  sent  against  the  crater,  the 
P.D.  is  diminished  to  exactly  the  same  extent  as  when  air  is  used. 

(5)  If,  on  the  other  hand,  nitrogen  is  sent  against  the  crater, 
no  diminution  of  the  P.D.  is  observable. 

(6)  If  air  or  oxygen  is  gently  blown  through  the  negative 
carbon,  so  that  it  cannot  get  direct  to  the  crater,  no  diminution 
of  the  P.D.  follows. 

Thus  there  can  be  no  shadow  of  doubt  that  the  sudden 
diminution  of  P.D.  that  accompanies  the  hissing  of  the  open  arc  is 
due  to  the  oxygen  in  the  air  getting  directly  at  the  crater  and  com- 
bining with  the  carbon  at  its  surface. 

It  only  remains  to  show  how  the  actual  hissing  sound  may  be 
produced  by  the  burning  of  parts  of  the  surface  of  the  crater. 
The  moment  after  this  burning  has  begun,  a  cloud  of  gas, 
formed  of  the  products  of  combustion,  must  spread  over  the 
burning  part,  protecting  it  momentarily  from  the  action  of  the 
air  as  effectually  as  the  carbon  vapour  had  hitherto  done. 
When  this  gas  is  dispersed  the  air  will  again  come  into  contact 
with  that  part  of  the  crater,  a  fresh  cloud  will  form,  and  the 
whole  action  will  start  de  novo.  Thus  a  series  of  rushes  and 
stoppages  of  the  air  will  take  place,  setting  up  an  irregular 
vibration  of  the  very  kind  to  cause  a  hissing  noise.  Not  only 
this,  however,  but,  since  the  crater  must  cease  to  burn  each 
time  that  it  is  protected  by  the  gas,  the  diminution  of  P.D. 
must  also  cease  to  exist  at  that  part,  since  its  cause  is  removed, 
and  the  P.D.  will,  therefore,  rise  momentarily.  Thus  an 


CAUSE  OF  HISSING  SOUND.  309 

oscillation  of  the  P.D.  between  the  carbons,  and,  consequently, 
of  the  electric  current  must  be  created,  corresponding  with  the 
oscillation  of  the  air  current. 

That  the  air  current  does  oscillate  when  the  arc  hisses  was 
proved  beyond  a  doubt  by  the  following  experiment.  One  end 
of  a  very  fine  single  fibre  of  asbestos  was  fastened  to  the  hole 
of  the  crucible  shown  in  Fig.  86  through  which  the  positive 
carbon  was  moved.  Sufficient  space  was  left  between  the  hole 
and  the  carbon  for  the  free  end  of  the  fibre  to  stretch  out 
horizontally  without  touching  the  latter.  While  the  arc  was 
silent  the  fibre  remained  fairly  motionless,  but  as  soon  as  hissing 
began,  instead  of  being  sucked  into  the  crucible,  as  it  wonld 
have  been  with  a  steady  inward  current  of  air,  it  vibrated 
rapidly  up  and  down,  thus  showing  the  oscillatory  character  of 
the  current. 

The  oscillation  of  the  electric  current  was  also  proved  beyond 
a  doubt,  by  Messrs.  Frith  and  Rodgers,*  in  1893  ;  and  it  has 
recently  been  shown,  graphically,  in  the  most  convincing 
manner  by  the  curves  published  by  Messrs.  Duddell  and 
Marchant.t  Mr.  Duddell  has  since  made  much  more  detailed 
curves  of  the  same  kind  which  will  shortly  also  be  published. 

Thus  we  have  seen  that  not  only  the  sudden  diminution  of 
the  P.D.  between  the  carbons,  but  every  other  phenomenon 
that  attaches  to  the  hissing  arc  may  easily  be  caused  by  the 
oxygen  of  the  air  getting  directly  at  the  crater,  and  combining 
with  the  carbon  at  its  surface. 


SUMMARY. 

I.  When  the  length  of  the  arc  is  constant  and  the  arc  is 
silent,   it   may  be   made  to    hiss    by    increasing   the   current 
sufficiently. 

II.  The  largest  current  that  will   maintain  a  silent  arc  is 
greater  the  longer  the  arc. 

III.  The  hissing  point  always  occurs  on  the  flat  part  of  the 
curve,  at  a  point  where  the  P.D.  changes  very  slightly  with 
change  of  current. 

*  Phil.  Mag.,  1896,  p.  407. 

f  Journal  lust.  Elec.  Eng.,  Vol.  XXVIIL,  pp.  78,  79. 


310  THE  ELECTRIC  AtiC. 

IV.  When  the  current  is  constant  and   the  arc  is  silent, 
shortening  it  will  make  it  hiss. 

V.  A  straight  line  law  connects  the  P.D.  at  the  hissing  point 
with  the  length  of  the  arc. 

VI.  With  a  given  pair  of  carbons  the  current  cannot  have 
more  than  a  certain  maximum  value  without  causing  the  arc  to 
hiss,  however  long  it  may  be. 

VII.  When  the  arc  begins  to  hiss,  the  P.D.  suddenly  falls 
about  10  volts  and  the  current  suddenly  rises. 

VIII.  For  the  hissing  arc  the  P.D.  is  constant  for  a  given 
length  of  arc,  whatever  the  current,  and  whether  the  carbons 
are  cored  or  solid. 

IX.  A  straight  line  law  connects  this  constant  P.D.  between 
the  carbons  with  the  length  of  the  arc,  when  both  carbons  are 
solid,  but  not  when  the  positive  is  cored. 

X.  A  straight  line  law  connects  the  diminution  of  P.D.  that 
accompanies  hissing  with  the  length  of  the  arc. 

XI.  The  longer  the  arc,  the  less  is  the  P.D.  between  the 
carbons  diminished  when  hissing  begins. 

XII.  About   two  thirds    of   the  diminution    of    P.D.,  when 
hissing   begins,   takes  place  at  the  junction  of   the  positive 
carbon  and  the  arc.     The  remainder  is  apparently  due  to  a 
diminution  of  the  resistance  of  the  arc  vapour,  and  none  to 
any  change  in  the  P.D.  between  this  vapour  and  the  negative 
carbon . 

XIII.  When    the    largest   silent    current    changes    to    the 
smallest  hissing  current  for  the  same  length  of  arc,  the  value 
of  that  smallest  hissing  current  depends  only  on  the  E.M.F.  of 
the  generator  or  the  resistance  in  the  circuit  outside  the  arc, 
whichever  is  fixed  first. 

XIV.  When  the  arc  is  silent  and  the  current   small,  the 
crater  presents  a  uniformly  bright  appearance,  but  when  the 
current  is  increased  sufficiently,  patches   of  bright  and  dark 
bands  appear  on  it,  whirling  and  oscillating  faster  and  faster 
as  the  current  is  increased. 

XV.  When   the  current  is  so  great   that  the   arc  is   near 
humming,  the  speed  of  revolution  is  too  great  to  be  detected 
by  the  eye,  and  it  continues  to  increase  to  about  450  revolu- 
tions a  second,  when  the  arc  begins  to  hiss. 


SUMMARY.  311 

XVI.  With  humming  and  hissing,  a  green  light  appears  in 
the  crater,  and  with  hissing,  clouds  partially  cover  the  crater ; 
and  the  carbon  vapour   becomes  flattened  out   between   the 
carbons. 

XVII.  With  a  short  hissing  arc  a  mushroom  forms  on  the 
end  of  the  negative  carbon. 

XVIII.  With  a  silent  arc  the  end  of  the  positive  carbon  is 
rounded,  and  the  crater  occupies  the  smallest  cross-section  of 
it.     With  a  hissing  arc  the  end  is  nearly  or  quite  cylindrical, 
except  where  the  crater  has  cut  it  away  obliquely. 

XIX.  Hissing  is  produced  by  the  crater  becoming  too  large  to 
occti]>y  t/te  end  only  of  the  positive  carbon,  and  by  its  therefore 
e,rtendi)ig  up  the  side. 

XX.  When  the  arc  is  enclosed  in  such  a  way  that  very  little 
or  no  air  can  get  to  it,  there  is  no  sudden  diminution  in  the 
P.D.  between  the  carbons,  even  with  currents  three  times  as 
great  as  would  produce  that  diminution  with  the  open  arc. 

XXI.  If,  however,  whether  the  air  is  excluded  or  not,  puffs 
of  air  are  sent  against  the  crater,  the  diminution  of  the  P.D. 
does   occur,    even    with    currents    much    smaller   than    would 
ordinarily  cause  hissing. 

XXII.  If,  instead  of  air,  oxygen  is  sent  against  the  crater, 
the  P.D.  is  diminished  to  exactly  the  same  extent  as  when  the 
air  is  used. 

XXIII.  If,  on  the  other  hand,  nitrogen  or  carbon  dioxide  is 
sent  against  the  crater,  no  diminution  of  the  P.D.  is  observable. 

XXIV.  If  air  or  any  of  the  other  gases  are  gently  blown 
through  the  negative  carbon,  so  that  they  cannot  get  direct  to 
the  crater,  710  diminution  of  the  P.D.  follows. 

XXV.  Thus  there  can  be  no  doubt  that  the  sudden  diminution 
of  P.D.  that  accompanies  the  hissing  of  the  open  arc  is  due  to  the 
oxygen  in  the  air  getting  directly  at  the  crater  and  combining  with 
the  carbon  at  its  surface. 

XXVI.  Hydrogen,  blown  against  the  crater  of  a  silent  arc, 
causes  hissing  and  a  diminution  of  about  6'6  volts  in  the  P.D. 
between  the  carbons,  when  the  arc  is  open  to  the  air.     When, 
however,  the  arc  is  enclosed,  so  that  air  is  excluded,  no  such 
effect  can  be  observed. 


CHAPTER    XL 


THE  LIGHT  EMITTED  BY  THE  ARC.  DIFFERENT  CANDLE  POWER 
IN  DIFFERENT  DIRECTIONS.  MEAN  SPHERICAL  CANDLE 
POWER  UNDER  DIFFERENT  CONDITIONS.  LUMINOUS  EFFI- 
CIENCY UNDER  VARYING  CONDITIONS.  How  TO  OBTAIN 
THE  MAXIMUM  LUMINOUS  EFFICIENCY  UNDER  ANY  GIVEN 
CONDITIONS. 

The  value  of  a  source  of  light  depends  upon  two  conditions — 
(1)  the  total  amount  of  light  that  it  emits,  (2)  the  distribution 
of  that  light.  It  is  absolutely  essential  to  know  both  these 
factors  in  order  to  judge  of  the  utility  of  the  source,  for  a 
large  total  flux  of  light  is  of  little  use  if  emitted  in  the  wrong 
direction,  and  a  light  may  be  all  in  the  right  direction,  but  so 
dim  as  to  be  practically  valueless.  Suppose,  for  instance,  that 
the  arc  would  only  burn  with  the  positive  carbon  underneath ; 
then,  however  brilliant  it  might  be,  it  would  be  useless  for 
street  lighting ;  for,  although  the  tops  of  our  houses  would 
be  well  illuminated,  the  streets  would  be  left  in  darkness. 
Again,  imagine  a  farthing  dip  in  a  ball-room :  though  every 
ray  were  utilised,  it  would  only  suffice  to  make  darkness 
visible.  What  we  want  to  know  about  a  source  of  light,  then, 
is  the  quantity  of  light  it  emits  and  the  direction  of  the  light. 

Some  sources  are  so  constituted  that  it  is  physically  im- 
possible to  utilise  all  the  light  they  emit.  The  very  conditions 
under  which  they  exist  cause  the  obstruction  of  some  of  their 
light.  Thus,  while  the  light  of  a  candle  or  a  gas  jet  is  practi- 
cally unobstructed,  in  paraffin  and  glow-lamps  part  of  the  light 
evolved  is  necessarily  absorbed  by  the  glass  covering  needed — 
in  the  one  case  to  create  a  sufficient  draught  of  air  to  com- 
pletely consume  the  oil,  and  in  the  other  to  maintain  a 
vacuum  round  the  filament.  In  the  arc  there  is  a  still  greater 
difference  between  the  quantity  of  light  evolved  and  the 


314  THE  ELECTRIC  ARC. 

amount  that  can  be  usefully  employed,  for  the  negative  carbon 
usually  obstructs  far  more  of  the  light  from  the  principal 
source — the  crater — than  would  be  absorbed  by  a  clear  glass 
covering.  Moreover,  with  every  change  in  the  current  or  the 
length  of  the  arc,  in  the  diameter  or  construction  of  either 
carbon,  the  form  of  the  negative  carbon  changes,  and,  conse- 
quently, the  amount  of  the  light  that  is  obstructed  changes 
also.  Hence  arise  many  complications  in  the  laws  governing 
the  light  of  the  arc,  which  vanish  more  or  less  completely 
when  the  amount  of  light  evolved  and  the  quantity  that 
escapes  and  becomes  perceptible  to  the  eye  are  studied 
separately. 

The  sources  of  light  in  the  arc  are  (1)  the  crater,  (2)  the 
remainder  of  the  hot  end  of  the  positive  carbon,  (3)  the  white- 
hot  spot  on  the  negative  carbon,  "  the  white  spot,"  as  I  have 
called  it,  (4)  the  remainder  of  the  hot  end  of  the  negative 
carbon,  (5)  the  arc  vapour.  I  shall  call  the  light  of  the  whole 
five  sources  together  the  light  of  the  arc,  and  shall  speak  of 
the  light  emitted  by  the  arc  proper  as  the  vapour  light,  or  the 
light  of  the  vapour. 

Not  only  the  quantity  but  the  proportion  of  the  whole  light 
emitted  by  each  of  the  sources  probably  varies  with  each 
current  and  length  of  arc,  as  well  as  with  the  construction  and 
thickness  of  either  carbon.  But  in  all  cases  by  far  the  larger 
part  of  the  light  is  due  to  the  crater,  the  next  greatest  source 
being  the  white  spot ;  and,  last  of  all,  the  hot  sides  of  the 
carbons  and  the  vapour,  which,  even  when  the  arc  is  long 
enough  to  "  flame,"  give  comparatively  little  'of  the  light. 
What  the  exact  proportions  are  under  any  given  set  of  -con- 
ditions, and  how  they  change  when  the  conditions  change, 
has  never  yet  been  accurately  determined ;  nor,  indeed,  has 
much  attention  been  paid,  as  far  as  separate  photometric 
measurements  of  intensity  are  concerned,  to  the  light  of  any 
other  part  of  the  arc  but  the  crater.  Sir  William  Abney 
discovered,  for  instance,  as  long  ago  as  1881,*  that  the  quantity 
of  light  emitted  per  square  millimetre  of  crater  was  practically 
a  constant  for  a  given  quality  of  carbon,  however  the  current 
and  the  length  of  the  arc  might  be  varied  ;  but  whether  the 
intrinsic  brilliancy  of  the  white  spot,  or  of  the  vapour,  is  also  a 
*  Phil.  Trans.,  1881,  Vol.  CLXXIL,  p.  890. 


. 

CANDLE  POWER  AND  AREA  OF  CRATER.         315 

constant,  has  never  been  determined.  Similarly,  it  is  known 
that  with  a  given  length  of  arc  the  area  of  the  crater  increases 
as  the  current  increases,  and  I  have  shown  (p.  154)  that  the 
area  of  the  crater  increases  also,  as  the  length  of  the  arc  is 
increased,  with  a  given  current ;  but  no  attention  whatever 
has  been  paid  to  the  variations  in  the  area  of  the  white  spot, 
which  I  have,  nevertheless,  found  to  depend  as  definitely  on 
the  current,  though  not  on  the  length  of  the  arc,  as  the  area 
of  the  crater  itself.  The  reason  of  this  neglect  is  obvious.  In 
the  ordinary  vertical  arc  with  the  positive  carbon  on  top  (which 
alone  we  are  now  considering)  the  light  from  the  white  spot 
must  principally  escape  upwards,  and  can  thus  be  of  little  use  in 
the  region  far  below  the  arc  for  which  the  light  is  needed.  Thus, 
though  this  white  spot  is  nearly,  if  not  quite,  as  brilliant  as 
the  crater  (though  far  inferior  to  it  in  extent),  the  light  from 
it  is,  in  a  sense,  unimportant.  The  light  emitted  by  the  arc 
vapour  is  also  small  compared  with  that  of  the  crater,  so  that 
it  also  has  received  very  little  attention.  In  determining  the 
light  emitted  by  the  arc  then,  the  important  points  to  consider 
are  (1)  the  quantity  of  light  given  out  by  the  crater,  and  (2)  the 
extent  to  which  this  light  is  obstructed  by  the  negative  carbon. 

It  must  always  have  been  noticed  from  the  first  that  the 
negative  carbon  cuts  off  more  or  less  of  the  brilliant  light 
emitted  by  the  crater ;  but  how  much,  under  any  given  con- 
ditions, was  never  made  clear  till  Mr.  Trotter*  put  the  whole 
matter  in  a  nutshell  by  enunciating  and  proving  experi- 
mentally the  delightfully  simple  theorem  that  the  great 
difference  observable  in  the  candle  power  of  the  arc  in  different 
directions  is  due  solely  to  the  different  amounts  of  crater 
visible  in  those  directions.  He  showed  that  in  directions  in 
which  the  view  of  the  crater  was  entirely  unobstructed,  the 
candle  power  varied  directly  as  the  apparent  area  of  the  mouth 
of  the  crater,  and  that  where  it  was  obstructed  by  the  negative 
carbon  the  candle  power  diminished  in  proportion  to  the 
increase  of  the  obstruction.  He  found  also  that  the  light 
emitted  by  all  parts  of  the  arc  and  carbons  except  the  crater 
was  practically  the  same  in  all  directions,  with  given  carbons, 
current,  and  length  of  arc,  as,  of  course,  it  would  have  to  be 
for  his  theorem  to  be  correct. 

*  The  Meet rk- ton,  1892,  Vol.  XXVIII.,  p.  687,  and  VoL  XXIX-Tp.  11. 


316  THE  ELECTRIC  ARC. 

The  Light  received  from  the  Crater  in  Different  Directions. 
Let  us  consider  the  light  and  the  obstruction — the  crater 
and  the  negative  carbon — separately.  Mr.  Trotter  began  by 
correcting  the  erroneous  impression  frequently  held,  that  the 
hollowing  of  the  crater  caused  the  light  to  be  concentrated 
and  cast  downwards.  He  pointed  out  that  the  same  amount 
of  light  was  received  from  the  crater  in  any  direction  as  would 
be  received  in  that  direction  from  a  disc  of  equal  brightness 
fitting  into  the  mouth  of  the  crater.  This  is  only  absolutely 
true  when  none  of  the  light  is  absorbed  in  its  passage  from  the 
surface  of  the  crater  to  its  mouth.  It  will  be  seen  later  that 
it  is  more  than  probable  that  this  condition  is  not  entirely 
fulfilled ;  but  the  error  thus  introduced  is  in  most  cases  so 
small  that  we  may  neglect  it,  and  consider  the  crater  as  a 
luminous  disc  of  area  equal  to  its  mouth.  Mr.  Trotter's 
theorem  is,  then,  that  with  the  exception  of  a  comparatively 
small  quantity  of  light,  which  is  constant  for  all  directions, 
the  candle  power  of  the  arc  in  any  direction  is  directly 
proportional  to  the  apparent  area  of  the  crater  as  seen  from 
that  direction. 

We  may  talk  about  the  apparent  area  of  the  crater  as  looked 
at  in  a  direction  instead  of  from  a  point,  because  the  diameter 
of  the  crater  is  always  so  small  compared  with  the  distance  of 
the  eye  or  the  photometer  screen  from  it  that  its  apparent  area 
is  the  same  from  all  points  in  any  one  direction.  Let  AB,  for 
instance  (Fig.  88),  be  the  diameter  of  the  crater,  and  EC  a 
direction  in  which  it  is  viewed,  then  if  the  eye  is  at  C,  the 
apparent  area  of  the  crater  will  depend  upon  the  angle  B  C  A, 
and  if  it  is  at  D  it  will  depend  upon  the  angle  B  D  A.  If 
D  and  C  are  both  very  far  from  A  B,  these  two  angles  will  be 
practically  equal,  and  so  the  apparent  areas  of  the  crater,  as 
seen  from  these  two  points,  will  be  equal  also.  For  the  same 
reason — the  smallness  of  the  crater  compared  with  its  distance 
from  the  eye — the  line  joining  the  point  from  which  it  is 
viewed  to  any  point  on  the  crater  may  be  called  the  direction 
in  which  it  is  viewed,  for  clearly  when  C  is  far  away,  CA, 
C  B  and  C  E  are  all  parallel. 

Mr.  Trotter  pointed  out  that,  when  there  is  no  obstruction 
the  apparent  area  of  the  crater  varies  directly  as  the  cosine  of 
the  inclination,  that  is,  as  the  cosine  of  the  angle  between  the 


APPARENT  AREA  OF  CRATER. 


317 


plane  through  the  mouth  of  the  crater  and  a  plane  per- 
pendicular to  the  line  joining  the  eye  to  the  crater.  In  other 
words,  the  apparent  area  of  the  crater  is  proportional  to  the 
cosine  of  the  angle  between  the  direction  from  which  it  is  viewed 


FIG.  88. — Disc  Viewed  from  a  Great  Distance. 

and  the  perpendicular  to  the  mouth  of  the  crater.  This  also  is, 
of  course,  only  strictly  true  when  the  diameter  of  the  crater 
is  small  compared  with  its  distance  from  the  eye.  A  complete 
mathematical  proof  of  it  is  given  in  the  Appendix  (page  441). 


318 


Til E  ELECTRIC  ARC. 


Mr.  Trotter's  experiments  were  very  simple,  but  they  were 
quite  conclusive  for  the  cases  he  tried.  The  apparent  area  of 
the  crater,  seen  from  different  directions,  was  measured,  and 
the  candle-power  of  the  arc  in  the  same  directions  taken,  and 
it  was  found  that  the  two  sets  of  values  both  varied  as  the 


(Trotter). 


60°. 


/  \ 

30°. 


50°.  20°. 

FIG.  89.— Tracings  of  normal  arc  If  full  size. 

cosine  of  the  inclination,  for  all  directions  in  which  the  view  of 
the  crater  was  unobstructed. 

Mr.  Trotter  pointed  out  that  when  the  radius  vector  of  a 
polar  curve  is  proportional  to  the  cosine  of  the  angle  between 


APPARENT  AREA  OF  CRATER, 


319 


it  and  the  fixed  line,  the  curve  is  a  circle,  of  which  the  pole  is 
one  point.  Thus,  he  argued,  a  polar  curve  with  a  line  pro- 
portional to  the  apparent  area  of  the  crater  as  radius  vector, 
and  the  inclination  of  the  crater  as  the  angle  between  the 
radius  vector  and  the  fixed  line,  must  form  a  part  of  a  circle. 
Hence,  the  candle-power  of  the  crater,  plotted  as  a  polar  curve, 
must  also  form  a  part  of  a  circle  for  those  directions  in  which 

(Trotter). 


30°.  15°. 

FIG.  90.— Tracings  of  Short  Arc  1|-  full  size. 

the  view  of  the  crater  is  unobstructed,  if  this  candle-power 
varies  directly  as  the  amount  of  crater  visible. 

The  tracings  of  the  crater  and  the  negative  carbon  that 
Mr.  Trotter  used  to  test  his  theory  are  given  in  Figs.  89  and  90. 
These  show  that  with  an  inclination  of  90°,  that  is,  when 
the  eye  was  in  a  horizontal  line  with  the  plane  of  the  crater, 
the  crater  could  not  be  seen  at  all,  as  one  would  expect.  With 


320 


THE  ELECTRIC  ARC. 


inclinations  of  from  90°  to  between  50°  and  40°,  the  crater  was 
entirely  unobstructed  by  the  negative  carbon,  and  with  smaller 
inclinations  the  obstruction  was  greater  the  less  the  inclination. 
The  apparent  areas  of  the  crater,  and  the  candle-power  of  the 
arc,  taken  from  the  same  points,  are  both  plotted  in  Figs.  91 
and  92,  the  angle  between  the  radius  vector  and  the  fixed  line 
being  made  equal  to  the  inclination  of  the  crater  in  each  case. 
Triangles  represent  areas  of  crater,  and  crosses  candle-power. 
It  will  be  seen  that  the  observations  of  areas  and  of  candle- 

(Trotter.) 


40° 


FIG.  91. — Curve  of  Areas  of  Crater  and  Candle-Power  of   Normal  Arc. 
A  =  area  and  x  =  candle-power.     The  scale  of  radii  is  arbitrary. 

powers  coincide  in  a  very  remarkable  manner  with  one  another, 
and  with  a  part  of  the  circle  which  is  the  polar  curve  connect- 
ing the  cosine  of  the  inclination  with  the  inclination. 

Fig.  93  shows  the  connection  between  candle-power  and 
apparent  area  of  crater,  from  different  directions,  with  rectan- 
gular co-ordinates,  ordinates  representing  candle-power  and 
abscissae  apparent  areas  of  crater.  The  points  lie  very  fairly 
well  in  a  straight  line  which  cuts  the  axis  of  candle-power  at 
about  100.  This,  therefore,  must  have  been  the  candle-power 


CANDLE  POWER  AND  AREA  OF  CRATER.         321 

of  the  white  spot,  the  glowing  ends  of  the  carbons  and  the 
vapour,  and  the  curve  shows  that  the  part  of  the  candle- 
power  of  the  arc  that  is  due  to  these  is  practically  the  same 
in  all  directions,  with  a  given  current  and  length  of  arc  and  a 
given  pair  of  carbons. 

Mr.  Trotter's  results  were  qualitative  rather  than  quantita- 
tive ;  his  candle-powers  were,  in  most  cases,  relative,  and  not 
absolute,  but  there  can  be  no  doubt,  nevertheless,  that  he 
proved  his  point,  and  that  the  variable  part  of  the  candle- 

( Trotter.) 


so' 


10  20  80 

FIG.  92. — Curve  of  Areas   of   Crater   and  Candle-Power  of  Short  Arc. 
A  =  area  and  x  =  candle-power.     The  scale  of  radii  is  arbitrary. 

power  of  the  arc  was  very  fairly  proportional  to  the  apparent 
area  of  the  crater  in  the  cases  he  tried.  This  carries  with  it, 
as  he  stated,  the  necessity  for  the  light  being  uniformly  dis- 
tributed over  the  crater  also ;  that  is,  his  experiments  show  that, 
roughly,  the  quantity  of  light  emitted  per  unit  surface  of  the 
crater  is  constant  over  the  whole  surface,  for  otherwise  the 
variable  part  of  the  candle-power  would  depend  upon  which 
part  of  the  crater  was  visible  from  any  point  as  well  as  upon 
how  much. 


322 


THE  ELECTRIC  ARC. 


Although  Mr.  Trotter's  experiments  show  that  the  light 
received  from  the  crater  is  fairly  uniform,  his  own  later 
experiments  and  mine  prove  that  it  cannot  be  entirely  so. 
For  when  a  part  of  the  crater  is  covered  with  the  swiftly 
whirling  figures  that  he  discovered  in  1894,  and  the  more 
slowly  moving  ones  that  I  showed  at  the  Institution  of  Electrical 
Engineers  in  1899,  it  is  quite  evident  that  more  light  per 

(Trotter.) 


muu 
900 

/ 

/ 

800 
700 
600 

/ 

/ 

/ 

/ 

800 
200 
100 

/ 

/ 

/ 

|  Light 

j  ^ 

rom  flai 
\  orange 

ie  of  arc 
parts.. 

• 

i 

20        40 


60 


80        100       120        140       160       180       200 

Relative  Areas. 
FIG.  93.— Areas  of  Crater,  and  Light  of  Normal  Arc. 

square  millimetre  must  be  received  from  the  entirely  bright 
parts  of  the  crater  than  from  the  parts  where  there  are  dark 
bands. 

Quantity  of  Light  Obstructed  by  Negative  Carbon. 

We  have  next  to  consider  how  far  the  light  emitted  by  the 

crater  is  obstructed  by  the  negative  carbon.     If  this  carbon 

were  of  constant  shape  for  all  currents  and  lengths  of   arc, 

cleaily  the  amount  of  light  obstructed  by  it  would  depend 


OBSTRUCTION  OF  LIGHT  BY  NEGATIVE  CARBON.  323 

simply  on  the  length  of  the  arc,  for  the  farther  the  negative  car- 
bon was  from  the  crater  the  less  crater  light  it  would  obstruct. 
This  is  by  no  means  the  case,  however.     As  has  already  been 
mentioned,  the  shape  of  the  negative  carbon  alters  with  every 
change  in  the  current  and  the  length  of  the  arc,  and  alters 
more,  for  a  given  change,  the  shorter  the  arc  and  the  smaller 
the  current.     With  short  arcs   and  large  currents  it  is  very 
sharply  pointed,  and  the  point  becomes  blunter  the  longer  the 
arc   and   the   smaller  the   current.      Take,  for  instance,  the 
diagrams  for  arcs  of  3mm.  in  Fig.  8  (p.  10).     There  is  con- 
siderably more  difference  in  form  in  the  negative  carbons  for 
currents  of  6  and  of  10  amperes  than  in  those  for  currents  of 
16  and  21  amperes.     Or,  take  the  6mm.  arc:  the  difference 
between    the    negative    carbons   for    6   and    16   amperes    is 
decidedly  greater  than  between  those  for  16  and  30  amperes. 
Again,  in  the  diagrams  for  10  amperes  in  the  same  figure,  the 
change    in   the  negative  carbon  caused  by  lengthening  the 
arc  from    1mm.    to    2mm.,    is  greater   than   that  caused   by 
lengthening  it  from  2mm.  to  3mm.,  and  with  a  current  of 
6  amperes  the  difference  between  the  negative  carbons  for 
1mm.  and  2mm.  is  greater  than  that  caused  by  lengthening 
the  arc  from  2mm.  to  as  much  as  6mm.     A  comparison  of  the 
diagrams  in  Figs.  7,  8  and  9  (pp.  9,  10  and  12)  shows  that  the 
shape  of  the  negative  carbon  depends  on  the  diameters  of  the 
carbons  as  well  as  on  the  current  and  the  length  of  the  arc. 

In  order  to  study  with  greater  ease  the  changes  in  the 
shape  of  the  negative  carbon,  some  of  the  diagrams  in 
Figs.  7,  8  and  9  have  been  enlarged.  In  Fig.  94  the  carbons 
and  the  current  are  constant,  or  nearly  so,  but  the  length  of 
the  arc  is  1mm.,  2mm.  and  6mm,,  going  from  left  to  right. 

There  is  a  certain  similarity  in  the  forms  of  all  three 
negative  carbons :  each  has  two  shoulders — a  small  one,  of 
which  the  diameter  is  about  the  same  as  that  of  the  crater, 
and  a  larger  one,  where  the  burning  away  of  the  sides  of  the 
carbon  ceases.  This  larger  shoulder  is  usually  of  rather 
greater  diameter  than  the  unburnt  part  of  the  carbon,  because 
of  the  ragged  fringe  of  frayed  carbon  that  sticks  out  from  its 
sides.  The  differences  in  the  forms  of  the  various  negative 
carbons  depend  chiefly  upon  the  relative  diameters  of  the  two 
shoulders  and  the  distance  between  them,  and  on  the  shape 

T2 


324 


THE  ELECTRIC  ARC. 


and  height  of  the  point  that  rises  above  the  smaller.  Let 
us  examine  more  closely  the  way  in  which  the  negative 
carbon  interferes  with  the  light  of  the  crater.  As  the  arc  is 
practically  an  axially  symmetrical  source  of  light,  we  may,  for 
theoretical  purposes,  examine  the  light  in  one  plane  passing 
through  the  axis  of  the  two  carbons,  and  whatever  is  true  of 
the  light  in  that  one  plane  will  be  true  of  the  light  in  all 
other  planes  passing  through  the  axis,  except  in  so  far  as  any 
error  is  introduced  by  the  carbons  not  being  strictly  in  line, 
or  the  arc  burning  on  one  side. 

Let  A  B  and  A  C  represent,  the  one  a  diameter  of  the  crater, 
and  the  other  a  line  in  the  same  plane,  drawn  from  the  end 


FIG.  94.— Shape  of  Negative  Carbon,  with  same  Current  but  Different 
Lengths  of  Arc. 

of  that  diameter  to  touch  the  negative  carbon,  The  angle 
between  these  two  lines  includes  all  the  directions  on  the 
right-hand  side  of  the  arc  from  which  an  eye  moving  in  the 
same  plane  as  the  two  lines  could  see  the  crater  unobstructed 
by  the  negative  carbon.  Hence,  the  angle  B  A  C,  or  the  mean 
of  the  two  corresponding  angles  on  either  side  of  the  arc,  in  the 
same  plane,  roughly  measures  that  part  of  the  crater  light 
that  is  unobstructed  by  the  negative  carbon. 

Next,  if  B  D  be  drawn  to  meet  the  lower  shoulder  of  the 
negative   carbon   in  D,  B  D  is  the  nearest   direction  to  the 


OBSTRUCTION  OF  LIGHT  BY  NEGATIVE  CARBON.  325 

vertical  in  which  any  of  the  crater  can  be  seen  at  all.  That 
is  to  say,  the  angle  E  B  D  is  the  largest  angle  that  the  line 
joining  the  eye  to  the  crater  can  make  with  the  horizontal  for 
any  portion  of  the  crater  to  be  visible.  We  now  have  in  the 
angle  B  A  C  a  rough  measure  of  the  total  quantity  of  light 
received  from  the  crater  in  one  plane  in  directions  in  which  it 
is  unobstructed  by  the  negative  carbon,  and  a  similar  rough 
measure  of  the  quantity  received  in  directions  in  which  it  is 
partially  obstructed  in  the  angle  B  F  A,  which  is  equal  to  the 
angle  E  B  D  minus  the  angle  BAG.  It  will  be  observed  that 
the  second  is  only  a  very  rough  measure  indeed,  for  the 
amount  of  light  obstructed  depends  on  the  shape  of  the 
negative  carbon  between  the  points  C  and  D,  even  more  than 
on  the  angle  BFA.  Take,  for  instance,  the  1mm.  and  2mm. 
arcs  in  Fig.  94,  and  compare  the  angle  F  A  G  in  the  one  with 
the  same  angle  in  the  other.  This  angle,  which  lies  between 
the  line  touching  the  point  of  the  negative  carbon  and  the  line 
touching  the  smaller  shoulder,  includes  all  the  directions  from 
which  only  a  very  little  of  the  crater  is  hidden.  Now,  in  the 
1mm.  arc  this  angle  is  more  than  four  times  as  great  as  in  the 
2mm.  arc,  and  in  the  6mm.  arc  it  does  not  exist  at  all,  for 
the  lines  A  C  and  A  G  coincide.  Hence,  although  the  unob- 
structed crater  light  is  much  less  in  the  1mm.  arc  than  in 
the  2mm.  arc,  that  which  is  only  slightly  obstructed  is  much 
greater  in  the  1mm.  arc,  and  it  is  thus  possible  that  the  total 
amount  of  light  received  from  the  crater  of  the  1mm.  arc  may 
be  as  great  as,  or  even  greater  than,  that  received  from  the 
crater  of  the  2mm.  arc. 

The  Light  emitted  by  a  very  short  Arc  is  greater  than  when  the 
Arc  is  longer,  with  a  large  Constant  Current. 

It  is,  of  course,  only  the  proportion  of  the  crater  light  that 
gets  out,  compared  with  the  whole  light  emitted  by  the  crater 
that  can  be  estimated  in  this  way ;  but  when  the  areas  of  two 
craters  are  equal,  or  nearly  so,  a  very  good  rough  comparison 
of  the  relative  mean  spherical  candle-powers  of  the  two  arcs 
can  be  made  by  comparing  the  sizes  of  the  angles  B  A  C,  C  A  G, 
and  E  BD  in  each.  JSow  the  1mm.  and  2mm.  arcs  in  Fig.  94 
have  craters  of  very  much  the  same  area;  for  although  (see 


326 


THE  ELECTRIC  ARC. 


p.  154)  this  area  does  increase  as  the  arc  is  lengthened,  even 
when  the  current  is  constant,  yet  the  increase  in  this  case  is  so 
small  that  I  have  calculated  it  to  be  only  about  a  half  per  cent. 
Thus  the  relative  candle-powers  of  the  two  arcs  may  well  be 
estimated  by  the  above  method,  which  seems  to  show  that, 
in  this  one  instance  at  any  rate,  the  mean  spherical  candle 
power  of  the  1mm.  arc  was  at  least  equal  to  that  of  the 
2mm.  arc.  This  conclusion,  so  contrary  to  the  generally 
accepted  ideas,  and  arrived  at  by  a  mere  examination  of  the 
shape  of  the  negative  carbon,  could  not,  however,  be  accepted 
without  reference  to  actual  candle-power  experiments.  Let  us 
see  what  these  say. 


Screen. 


SCALE    OF    FEET 


I 


.i.  Arc. 


FIG.  95.— Side  View  of  Three  Mirrors,  A,  B  and  C,  throwing  the  Light  of 
the  Arc  through  a  Slit  on  to  the  Screen. 

Table  L.  shows  the  results  of  the  experiments  on  the  mean 
spherical  candle-power  of  the  arc  made  for  the  Paper  read  by 
Prof.  Ayrton  at  the  Electrical  Congress  at  Chicago  in  1893. 
They  were  obtained  by  taking  what  I  may  call  a  sample  of 
the  light  with  each  current  and  length  of  arc.  The  arc  was 
enclosed  in  a  light-tight  box  (of  which  one  side  is  seen  in 
elevation  in  Fig.  95),  and  a  wedge  of  light  was  allowed  to 
escape,  through  a  slit  of  constant  width,  long  enough  to 
allow  the  light  in  all  directions  in  one  vertical  plane  to  pass. 
This  wedge  of  light  was  received  on  a  screen  of  white 
blotting  paper  (Fig.  96),  and  in  order  that  the  whole  of  the 
light  in  the  one  vertical  plane  in  which  it  was  being  measured 


MEASUREMENT  OF  THE  LIGHT.  327 

g  should   be   collected   on   the   screen,  the 

.$  lower  part  of  the  light  was  reflected  from 

the  three  plane  mirrors  A,  B  and  C 
(Fig.  95)  on  to  the  screen.  From  the 

-fib  blotting  paper  the  light  was  reflected  on 

to  the  fixed  photometer  screen,  and  was 
compared  with  that  of  a  2  c.p.  Methven 
Standard,  which  was  movable  along  a 
|  2  bar  graduated  directly  in  mean  spherical 

candles.  Corrections  were  made  for  the 

£  light  absorbed  by   the   mirrors   and    the 

2  to       blotting  paper,  and  thus  the  mean  spheri- 
g  -^        cal  candle-power  for  each  arc  was  obtained 

fl    ^|j      *ls  at   one  reading,   or  rather  in  one  series 

pq  -^  of   readings,  for  the  mean  of  from  6  to 

"^  jB  12  readings  was  taken  in  each  case.     The 

o  %  carbons  employed  were  13mm.  cored  posi- 

J  7,  tive  and  llmm.  solid  negative. 

°  «  For  currents  of  4,   7  and  10  amperes, 

g  o  the    candle-power   of    the    2mm.    arc    is 

J'g  greater  than  that  of  the  1mm.  arc,  but 
for  currents  of  15  and  20  amperes  it  is 
considerably  less,  and  with  a  current  of 

J  a  32  amperes  the  1mm.  arc  gives  more  light 

j§  &  than  the  2mm.   arc  does  with  a  current 

w  «  of  32'5    amperes.       Thus   with    currents 

|  £  that  are  fairly  small  for  the  sizes  of  the 

^  .B  carbons,  the  longer  arc  gives  the  larger 

3  £  amount  of  light,   but  for  currents  great 
.3  ^  enough   for    the    negative   carbon    to   be 
,2  HH~  sharply  pointed,  as  it  was  in  Fig.  94,  the 

shorter  arc  does  actually  give  the  larger 
amount  of  light.  These  experiments, 
therefore,  confirm  the  conclusions  gathered 
from  a  comparison  of  the  shapes  of  the 
negative  carbons,  and  show  that  with 
short  arcs  and  large  currents  the  candle- 
§  power  of  the  arc  may  first  diminish 

and   then   increase   again   as    the   arc   is 
lengthened. 


328 


THE  ELECTRIC  ARC. 


Table  L. — Mean  Spherical  Candle-power  of  Arcs  of   Different 

Lengths  with  various  Constant  Currents. 
Carbons:  Positive,  I3mm.,  cored;  neijati-ce%  llwiw.,  solid. 


Current  in 
Amperes. 

Mean  Spherical  Candle-power. 

1mm. 

2mm. 

3mm.            4mm. 

6mm. 

4 

70 

103 

78               105 

6 

238 

247 

7 

270 

280 

353 

326 

10 

560 

700 

736 

900 

11 

730 

15                 1,220 

904 

1,087 

1,480 

1,180 

20 

1,754 

1,586 

1,714 

2,300 

1,914 

23-5 

., 

1,874 

23-75 

3,204 

24 

., 

2,486 

25 

,. 

3,332 

32                 2,880 

3,600 

32-5 

2,600 

34 

.  , 

3,870 

35 

... 

4,732 

... 

It  seems  probable  that  the  length  of  arc  with  which  the 
candle-power  is  a  minimum  diminishes  as  the  current 
diminishes,  with  carbons  of  any  given  size.  For  the  smaller 
the  current  the  shorter  must  be  the  arc  in  order  that  the 
negative  carbon  should  have  a  sharp  point  Thus  it  is  most 
likely  that  if  Prof.  Ayrton's  experiments  had  been  carried  on 
with  arcs  of  less  than  1mm.,  a  minimum  value  for  the  candle- 
power  with  a  current  of  10  amperes  would  have  been  found 
for  some  length  of  arc  between  Omm.  and  1mm.  When  the 
current  is  very  small  for  the  sizes  of  the  carbons,  however,  the 
negative  carbon  never  becomes  sharply  pointed,  however  short 
the  arc  may  be,  and  in  that  case  the  light  obstructed  by  the 
negative  carbon  must  steadily  increase,  as  the  arc  is  shortened, 
till  the  carbons  touch.  The  curves  in  Fig.  97,  which  are 
plotted  from  Table  L.,  show  very  clearly  how  the  mean  spherical 
candle-power  decreases  and  then  increases  again  with  the  short 
arcs  and  large  currents. 

Among  the  very  complete  and  beautiful  series  of  experiments 
on  the  total  flux  of  light  emitted  by  the  direct  current  arc, 


CANDLE  POWER  AND  LENGTH  OF  ARC. 


329 


made  by  M.  Blondel,*  and  published  in  1897,  were  several 
in  which  the  current  was  kept  constant  and  the  arc  was 
lengthened  from  0  to  many  millimetres.  M.  Blondel  plotted 
curves  connecting  the  flux  of  light  with  the  P.D.  between  the 
carbons  instead  of  with  the  length  of  the  arc,  and  hence  the 
phenomenon  under  discussion  escaped  his  observation.  Never- 
theless, indications  of  it  are  not  wanting  in  his  experiments, 

(Ayrton.) 


4,500 
4,000 
3.500 
3.0CO 
2,500 
2,000 
1,500 
1,000 


10  Arrips 


Length  of  Arc  In  Millimetres. 

Flu.  97. — Curves  connecting  Mean  Spherical  Candle  Power  with  Length  of  Arc. 
Carbons  :    Positive,  3mm.,  cored  ;  Negative,  13mm.,  solid. 

notably  in  the  two  curves  in  Fig.  98,  which  are  plotted  from 
the  numbers  given  by  M.  Blondel  for  Curves  I.  and  III.  in 
Table  III.,  p.  296,  of  his  articles. 

M.  Blondel's   method   of   measurement   was   the    same    in 
principle  as  Prof.  Ayrton's.     He  placed  the  arc  in  the  centre 
of   an  opaque  sphere,  on  opposite   sides  of   which  were   two 
*  L'Edairge  Elcctriquc,  1897,  Vol.  X.,  pp.  289,  496,  539. 


330 


THE  ELECTRIC  ARC. 


vertical  openings  of  18°  each  (Fig.  99).  The  whole  of  the 
light  that  escaped  from  these  two  slits  was  caught  by  an 
elliptic  mirror  M  (Fig.  100),  and  reflected  on  to  a  screen  of 
white  blotting  paper,  and  the  illumination  of  this  screen  was 
measured  by  means  of  the  "  Universal  Photometer,"  invented 
by  M.  Blondel  himself. 

(Blonde). ) 


12,000 


11,000 


10,000 


8,000 


7,000 


6,000 


14/IJ 


1  2  3 

Length  of  Arc  in  Millimetres. 

FIG.  98. —  Curves  connecting  Total  Light  emitted  with  Length  of  Arc. 
Positive  Carbon  cored  ;  negative  solid. 


M.  Blondel  preferred  to  measure  the  total  flux  of  light 
emitted  by  the  arc  rather  than  the  mean  spherical  candle 
power,  and  the  unit  he  employed  was  the  "  lumen,"  or  the 
total  flux  produced  by  a  source  having  a  uniform  intensity  of 
one  decimal  candle  in  a  solid  angle,  cutting  off  one  square 
millimetre  of  surface  from  a  sphere  of  radius  1mm.  As  the 
total  flux  of  light  emitted  by  a  source  is  numerically  equal  to 


BLONDEUS  APPARATUS  FOR  MEASURING  ARC  LIGHT.  331 

4?r  times  the  mean  spherical  candle  power,  M,  Blondel's 
numbers  have  only  to  be  divided  by  4?r  to  give  the  mean 
spherical  candle  power  of  the  arc  in  decimal  candles,  a  unit 


FIG.  99.— Apparatus  employed  by  M.  Blondel  in  Measuring  the  Total 
Light  emitted  by  the  Arc. 


,.<'-\r 


FIG.  100. — Arrangement  of  Apparatus  used  by  M.  Blondel. 
=  Arc,  M  =  Lunienonieter,  G  — Diffusing  Screen  of  White  Blotting  Paper, 
P  =  Photometer  Screen . 


332  THE  ELECTRIC  ARC. 

which  is  one-twentieth  part  of  the  Violle  unit.  As  this  unit 
is  not  universally  adopted,  however,  it  will  be  better  to  leave 
M.  Blondel's  results  in  lumens. 

For  the  upper  curve  in  Fig.  98,  the  carbons  employed  were 
"Nanterre,"  8mm.  cored  positive  and  6mm.  solid  negative. 
For  the  lower  curve  they  were  both  10mm.,  the  positive  cored 
and  the  negative  solid.  The  constant  current  was  10  amperes 
in  both  cases.  Both  curves  show  a  tendency  on  the  part  of 
the  light  emitted  to  diminish  or  at  most  to  remain  constant 
as  the  length  of  the  arc  is  increased  from  1mm.  to  2mm.  in 
the  one  case,  and  from  0-5mm.  to  1mm.  in  the  other.*  Thus 
M.  Blondel's  experiments  also  confirm  the  conclusion  reached 
by  a  simple  examination  of  the  diagrams  of  arcs  and  carbons, 
in  Fig.  94,  viz. :  that  with  certain  currents  the  lighting  power 
of  the  arc,  after  increasing  at  first  as  the  carbons  are  sepa- 
rated, diminishes  or  remains  stationary  as  the  arc  is  further 
lengthened,  and  then  increases  again. 

With  a  Constant  Current  the  Illuminating  Power  of  the,  Arc, 
Increases  to  a  Maximum  as  the  Arc  is  Lengthened,  and  then 
Diminishes  again. 

To  return  to  Fig.  94.  When  once  the  arc  is  long  enough 
for  the  point  of  the  negative  carbon  to  have  become  quite 
blunt  and  round,  it  is  plain  that  lengthening  the  arc  can  only 
enlarge  both  the  angles,  BAG  and  EBD,  on  which  the 
amount  of  crater  light  that  escapes  depends.  We  should,  there- 
fore, gather  from  this  figure  that  the  amount  of  light  received 
from  the  crater  must  increase  continually  as  the  arc  is 
lengthened  beyond  about  2mm.  •  and  if  Mr.  Trotter's  theorem 
is  correct  in  all  cases,  it  follows  that  the  candle  power  of  the 
arc  must  also  increase  continuously  as  the  arc  is  lengthened. 
To  see  whether  this  is  so,  we  must  turn  again  to  Fig.  97, 
taken  from  Prof.  Ayrton's  experiments.  These  curves  do  not 
seem  to  bear  out  the  deduction  made  from  the  shape  of  the 
negative  carbon,  for  they  prove  that,  far  from  increasing  con- 
tinually as  the  arc  is  lengthened,  the  illuminating  power  of 

*  The  lengths  of  arc  corresponding  with  P.Ds.  of  43 '5  volts  in  the 
upper  curve  and  48'7  volts  in  the  lower  were  not  given  by  M.  Blondel, 
and  were  therefore  found  by  plotting  the  curves  connecting  the  other 
P.Ds.  with  the  corresponding  lengths  of  arc  in  each  case. 


TOTAL  LIGHT  AND  LENGTH  OF  ARC. 


333 


the  arc  increases  only  till  it  is  of  a  certain   length,  and  then 
diminishes  again  as  it  is  further  lengthened.     This  most  inte- 


resting  and  important  point  was  first  noticed  by  Prof.  Ayrton, 
who  announced  it  in  the  Paper  he  read  before  the  Electrical 


334 


THE  ELECTRIC  ARC. 


Congress  at  Chicago  in  1893.  At  the  same  time  Prof.  Carhart 
mentioned  that  he  had  found  the  luminous  intensity  of  the  arc 
to  be  a  maximum  with  a  certain  definite  P.D.  between  the  carbons , 


the  P.D.  depending  on  the  nature  and  size  of  the  carbons. 
As  the  P.D.  between  the  carbons,  for  any  particular  current,  is 
determined  by  the  length  of  the  arc,  it  is  plain  that  the  two 


TOTAL  LIGHT  AND  LENGTH  OF  ARC.  335 

discoveries  were  identical,  though  I  shall  show  later  that 
Prof.  Ayrton's  was  the  more  correct  way  of  putting  it,  and 
that  the  maximum  illuminating  power  depends  directly  on  the 
length  of  the  arc,  and  therefore  only  indirectly  on  the  P.D. 
between  the  carbons. 

M.  Blonde],  as  I  have  mentioned  before,  drew  no  curves 
connecting  the  length  of  the  arc  with  any  of  the  other  variables, 
but,  from  the  tables  he  gave  of  the  results  of  his  experiments, 
I  have  drawn  the  curves  in  Figs.  101  and  102,  connecting  the 
total  light  emitted  by  the  arc  with  its  length.  For  Fig.  101 
both  carbons  were  solid,  and  their  sizes  varied  from  8mm.  and 
6mm.  to  16mm.  and  14mm.,  while  for  Fig.  102  the  positive 
carbon  was  cored  and  the  negative  solid,  and  their  sizes  varied 
from  8/6  to  18/14.  (This  is  a  very  convenient  way,  adopted  by 
M.  Blondel,  of  denoting  the  sizes  of  carbons.  The  left-hand  figure 
always  gives  the  diameter  of  the  positive  carbon  in  mm., 
and  the  right-hand  that  of  the  negative.)  The  current  was 
10  amperes  in  all  cases.  In  both  sets  of  curves,  in  every  case 
where  the  arc  was  made  sufficiently  long,  the  light  flux 
increased  to  a  maximum  and  either  remained  stationary  or 
diminished  as  the  arc  was  further  lengthened.  Thus  both 
Prof.  Ayrton's  and  M.  BlondePs  experiments  contradict  the 
evidence  of  the  diagrams  of  the  arc  and  carbons,  and,  in  order 
to  find  out  where  the  error  arises,  it  will  be  well  to  inquire  a 
little  more  in  detail  into  the  manner  in  which  the  most 
important  part  of  the  light — the  crater  light — varies  when  the 
current  is  kept  constant  and  the  arc  is  lengthened. 

For  this  purpose  the  diagrams  in  Fig.  103  will  be  found 
useful.  They  were  taken  from  arcs  of  Jmm.,  1*1  mm.,  2mm., 
3 '2mm.  and  6*6mm.,  burning  between  18mm.  cored  and  15mra. 
solid  carbons,  with  a  constant  current  of  20  amperes  flowing. 
On  the  assumption  that  Mr.  Trotter's  theorem  was  true  for  the 
arcs  from  which  these  diagrams  were  taken,  it  will  be  possible, 
with  the  help  of  Rousseau's  method  of  finding  the  total  light 
received  from  an  axially  symmetrical  source,  to  construct 
figures  of  which  the  areas  will  be  proportional  to  the  total 
quantity  of  light  received  from  the  craters  of  the  arcs.  Then, 
taking  the  number  of  square  millimetres  in  each  area  as  abscissa, 
and  the  corresponding  length  of  arc  as  ordinate,  we  shall  be 
able  to  draw  the  curve  connecting  the  total  quantity  of  light 


THE  ELECTRIC  ARC. 


1 


s    a 

Q    a 


s  ! 

I  a 
£  a 
S  s 

I  1 


UNOBSTRUCTED  CRATER  LIGHT.  337 

received  from  the  crater  with  the  length  of  the  arc,  for  the 
constant  current  of  20  amperes.  If,  then,  to  each  ordinate 
we  add  a  length  equivalent  to  the  quantity  of  light  received 
from  the  remaining  four  sources  in  the  arc  of  corresponding 
length,  we  should,  if  our  premises  and  measurements  have  been 
correct,  get  a  curve  of  the  same  general  form  as  those  in 
Figs.  97  and  102. 

Rousseau's  figures*  can  only  be  drawn  for  axially 
symmetrical  sources  of  light,  and  although  the  arc  is  this 
theoretically,  yet  it  is  so  in  theory  only,  for  the  carbons  are 
rarely  perfectly  in  line,  and  consequently  the  arc  is  seldom 
quite  central.  To  minimise  this  source  of  error,  we  shall  use 
only  measurements  which  are  the  mean  of  the  measurements 
made  on  either  side  of  the  diagram  in  each  case.  For  instance, 
instead  of  taking  the  angle  BAG  (Fig.  103)  as  the  angle 
containing  all  the  directions  from  which  the  whole  crater  can 
be  seen,  we  shall  take  the  mean  of  the  two  angles  BAG  and 
A  B  H  ;  and  so  on  with  all  the  other  measurements. 

To  Find,  from  a  Diagram  of  the  Arc  and  Carbons,  a  Figure 
proportional  to  the  Total  Amount  of  Light  received  from 
the  Crater. 

Let  us  first  consider  the  figure  that  would  represent  the 
total  light  received  from  the  crater  if  none  of  it  were  cut  off  by 
the  negative  carbon.  Let  A  (Fig.  104)  be  the  centre  of  the  mouth 
of  the  crater.  The  distance  between  the  crater  and  any  point 
at  which  the  light  from  it  is  measured  is  always  so  great, 
compared  with  the  diameter  of  the  crater,  that  the  light  may 
all  be  considered  to  come  from  one  point.  Thus,  by  Trotter's 
theorem,  we  have  to  find  the  total  light  received  from  a 
point  A,  when  the  quantity  of  light  received  in  any  direction 
is  proportional  to  the  cosine  of  the  angle  that  that  direction 
makes  with  the  vertical,  the  unit  quantity  of  light  being  the 
light  emitted  by  one  square  millimetre  of  crater. 

With  centre  A  and  unit  radius  describe  the  circle  BCD, 
cutting  the  horizontal  at  B  and  D  and  the  vertical  at  C. 
Draw  the  tangents  B  E  and  C  E,  and  produce  C  E  to  F,  making 

*  A  detailed  description  of  the  manner  in  which  these  figures  are 
drawn  to  represent  the  total  light  received  from  an  axially  symmetrical 
source  is  given  in  the  Appendix  (p.  448), 


338 


THE  ELECTRIC  ARC. 


EF  proportional  to  the  light  that  would  be  received  from  the 
crater  in  a  vertical  direction,  i.e.,  proportional  to  the  area  of 
the  crater.  Let  A  G  be  another  direction  from  which  the  light 
is  measured,  and  draw  G  H  K  parallel  to  C  F,  making  H  K  pro- 
portional to  the  light  received  in  the  direction  A  G.  Join  F  K 
and  KB,  and  draw  GM  parallel  to  AC.  Then  by  Trotter's 

theorem 

HK_cosGAC 

E  *'         cos  0 
GM 


C  E 

FIG.  104. — Figure  used  in  finding  Total  Light  received  from  Crater  if 
none  were  obstructed  by  Negative  Carbon. 

Therefore  B,  K,  and  F  are  in  one  straight  line,  and  B  F  must 
be  the  locus  of  the  ends  of  all  lines  drawn  in  a  manner  similar 
to  H  K,  each  proportional  to  the  light  received  from  the  crater 
in  some  given  direction  between  A  B  and  A  C.  But  the  figure 
representing  the  total  light  received  from  the  source  in  one 
plane  is  that  which  is  included  between  B  E,  E  F,  and  this 
locus.  Hence  the  triangle  B  E  F  must  be  the  figure  of  which 
the  area  is  proportional  to  the  whole  light  that  would  be 
received  from  the  crater  in  one  plane  if  none  of  it  were  cut  off 
by  the  negative  carbon,  and  2?r  x  area  B  E  F  is  the  total 
quantity  of  light  that  would  be  received  from  the  crater  in  all 
directions  if  none  were  cut  off  by  the  negative  carbon.  We 
have  thus  the  means  of  drawing  a  series  of  triangles,  of  which 
the  areas  would  represent  the  total  light  that  would  be 
received  from  the  craters  of  the  arcs  of  which  diagrams  are 


AREA  PROPORTIONAL  TO  TOTAL  CRATER  LIGHT.  339 

given  in  Fig.  103,  if  none  of  the  light  were  cut  off  by  the 
negative  carbon.  We  have  only  to  draw  triangles  having  their 
bases  proportional  to  the  areas  of  the  craters  in  the  diagrams 
and  their  heights  all  equal  to  B  E. 

In  order  to  compare  the  quantities  of  light  actually  received 
from  the  craters,  however,  this  is  not  sufficient,  we  must 
know  what  part  of  the  light  is  cut  off  by  the  negative  carbon. 
To  find  this,  let  BAG  (Fig.  105)  be  the  mean  of  the  two 
angles  B  AC  and  ABH  in  1,  Fig.  103,  and  let  BAN  be 
the  mean  of  the  two  angles  E  B  D  and  K  A  M  in  the  same 
figure.  Then  the  triangle  BHK  represents  the  whole  light 
received  from  the  crater  in  directions  in  which  the  whole  crater 
can  be  seen,  and  no  light  will  be  received  from  it  at  all  in  any 
direction  nearer  to  the  vertical  than  AN.  Therefore  the 


c  E  F 

FIG.  105. — Figure  proportional  to  Total  Light  received  from  Crater. 

figure  representing  the  total  light  received  from  the  crater 
when  part  of  it  is  cut  off  by  the  negative  carbon  must  be 
bounded  by  P  B,  B  K,  and  a  curve  which  starts  at  K  and 
ends  at  P.  One  point  on  this  curve,  if  well  chosen,  will  be 
sufficient  to  show  what  the  shape  of  the  curve  must  be,  for  we 
know  that  the  occultation  produced  by  the  negative  carbon 
must  both  increase  and  diminish  quite  gradually,  so  that  the 
curve  must  join  both  B  K  and  B  P  quite  smoothly.  The  best 
point  to  take  is  that  belonging  to  the  direction  in  which  the 
occultation  begins  to  be  serious,  the  point  corresponding  with 
the  direction  that  just  touches  the  larger  shoulder  of  the 
negative  carbon.  Let  A  Q  (Fig.  105)  be  this  direction,  then 
RS  is  the  line  representing  the  total  light  that  would  be 
received  from  the  crater  in  the  direction  A  Q  if  none  of  it  were 

22 


340  THE  ELECTRIC  AEG. 

cut  off  by  the  negative  carbon.     To  find  how  much  of  the  light 
in  this  direction  is  cut  off,  we  must  turn  to  Fig.  106. 

Let  AB  be  the  direction  in  which  the  light  is  being  received, 
and  let  C  D  be  the  tangent  to  the  negative  carbon  that  is 
parallel  to  A  B.  Then,  since  both  eye  and  photometer  screen 
are  far  from  the  crater,  all  the  rays  of  light  that  reach  the  eye 
from  the  crater  will  be  parallel  to  A  B,  and  all  rays  parallel  to 
A  B  that  enter  the  negative  carbon  will  be  cut  off  from  the  eye. 
The  outermost  of  these  rays  are  those  that  just  touch  the 
negative  carbon,  so  that  to  determine  what  region  of  the  crater 
is  obscured  by  the  negative  carbon  from  an  eye  looking  at  it 


FIG.  106.  —To  find  the  Quantity  of  Light  obscured  by  the  Negative 
Carbon  in  any  one  direction. 

in  the  direction  BA,  we  must  find  what  is  the  area  of  the 
crater  that  is  cut  off  by  these  tangent  rays.  The  true  area  of 
this  part  is  that  which  would  be  cut  off  from  the  crater  by  the 
horizontal  section  of  the  negative  carbon  through  D,  if  it  were 
moved  parallel  to  itself  along  the  line  D  C.  The  apparent  area, 
to  which  the  light  cut  off  is  proportional,  is  the  true  area 
multiplied  by  cos  D  C  H,  where  C  H  is  the  vertical.  As  all 
horizontal  sections  of  the  negative  carbon  are  practically 
circular,  this  true  area  would  be  that  cut  off  from  the  crater 
by  a  circle  in  the  same  plane,  having  C  F  =  D  G  for  its 
diameter,  To  find  this  area,  let  A  E,  AC,  OF  (Fig.  107)  be 


AREA  OF. GRATER  OBSCURED  BY  NEGATIVE.      341 

equal  to  the  corresponding  lengths  in  Fig.  106,  and  draw  the 
circle  E  G  H,  representing  the  area  of  the  mouth  of  the  crater, 
and  having  B  for  its  centre,  and  draw  F  G  H  equal  to  the  area 
of  the  cross-section  of  the  negative  carbon  at  D,  and  having  D 
for  its  centre.  Then  A  G  C  H  is  the  area  of  that  part  of  the 
crater  from  which  the  rays  in  the  direction  A  B  (Fig.  106)  are 
cut  off  by  the  negative  carbon. 


FIG.  107. — Geometrical  Construction  for  the  Area  of  Crater  obscured  by 
the  Negative  Carbon  in  any  one  direction. 


To  find  this  area,   draw  G  H  meeting  A  C  in  K,  and  join 
BG,  BH,  DG,  and  D  H. 
Let  r  =  A  B,  the  radius  of  the  mouth  of  the  crater. 

r'=  CD          ,,  „       horizontal  section  through  D. 

x  =  AC 

y  =  G  K  or  K  H. 
Let  «  be  the  angle  G  B  H  in  degrees,  and 

a'  GDH 


Then  the  area  A  G  H  is 


-  G  K,  K  B  ; 


the  area  C  G  H  is  ~r^-  G  K,  D  K  ; 
loU 

/.  the  area  A  G  C  H  =   a7r  r2  +  "0%'2  -  G  K  (B  K  +  K  D) 
180        180 


180 


r2  +  aV2)  - 


342  THE  ELECTRIC  ARC. 

Thus  the  required  area  has  been  found  in  terms  of  quantities, 
all  of  which  are  easily  obtainable  for  any  given  arc  by  drawing 
such  a  figure  as  Fig.  107  from  a  diagram  such  as  those  in 
Figs.  94  and  106. 

The  ratio  of  the  above  area  to  the  area  of  the  crater  is  the 
ratio  of  the  part  of  the  crater  light  cut  off  in  the  direction 
AB  (Fig.  106)  to  the  whole  light  emitted  in  that  direc- 
tion. If,  then,  AQ  (Fig.  105)  represents  the  direction  AB 
(Fig.  106)  i.e.,  if  the  angle  B  A  Q  (Fig.  105)  =  the  angle  E  A  B 
(Fig.  106),  then,  to  find  what  part  of  the  line  R  S  represents 
the  light  received  from  the  crater  in  the  direction  A  B  we 
must  take  a  point  T  such  that  S  B,  ;  S  T  ;  \  area  of  crater 
(Fig.  106)  :  area  GAHC  (Fig.  107),  and  the  curve  bounding 
the  figure  representing  the  total  light  received  from  the  crater 
must  pass  through  T.  We  now  have  four  points,  B,  K,  T 
and  P,  through  which  the  curved  part  of  the  figure  must 
pass,  and  thus  we  can  draw  the  figure  B  K  T  P  R  H,  of  which 
the  area  is  proportional  to  the  total  light  received  from  the 
crater  in  one  plane. 

The  numerical  value  of  the  total  light  received  from  the 
crater  in  all  directions  is  2?r  x  area  B  K  T  P  R  H,  when  the 
unit  of  light  is  the  quantity  of  light  emitted  by  a  square 
millimetre  of  crater.  If,  however,  we  take  as  our  unit  of 
light  the  quantity  of  light  emitted  by  a  square  millimetre  of 
crater  multiplied  by  2?r,  the  area  B  K  T  P  H  (Fig.  105)  will 
then  represent  the  total  light  received  from  the  crater  in  all 
directions  in  those  units. 

Curves  deduced  from  Diagrams  in  Fi<j.  103  connecting  Total  Light 
received  from  Crater  and  Total  Light  from  All  Sources  with 
Length  of  Arc. 

From  the  diagrams  in  Fig.  103  we  can  thus  find  figures 
similar  to  Fig.  107,  proportional  to  the  total  light  received 
from  the  crater  for  arcs  of  0'5mm.,  I'lmm.,  2mm.,  3 -2mm. 
and  6 -6mm.  when  the  positive  carbon  was  18mm.  cored,  and 
the  negative  15mm.  solid,  and  the  current  was  20  amperes. 
Then,  by  taking  distances  proportional  to  these  as  ordinates, 
and  the  corresponding  lengths  of  arc  as  abscissa?,  we  can 
draw  the  curve  connecting  the  total  light  received  from  the  crater 
with  the  length  of  the  arc  on  the  assumption  that  ilw  quantity 


TOTAL  LIGHT  &  LENGTH  OF  AUG  FROM  DIAGRAMS.  343 

of  light  emitted  ly  the  crater  per  square  millimetre  of  surface  is 
constant,  with  a  constant  current,  whatever  the  length  of  the  arc. 

This  curve  is  given  in  ABC  (Fig.  108),  and  it  is  obvious 
from  it  that  it  is  no  diminution  in  the  light  received  from  the 


crater,  as  the  arc  is  lengthened  after  a  certain  distance,  that 
causes  the  total  light  received  from  the  arc  to  diminish.  On 
the  contrary,  the  total  light  received  from  the  crater  increases 


344  TEE  ELECTEIC  ARC. 

continuously  as  the  arc  is  lengthened  with  these  particular 
carbons  and  this  current.  The  curve  does  not  pass  through 
the  zero  point,  because  length  of  arc  0  does  not  mean  that  the 
carbons  are  touching,  but  that  the  tip  of  the  negative  carbon 
is  in  the  same  plane  as  the  mouth  of  the  crater.  And  when 
the  carbons  are  so  close  the  first  is  always  smaller  than  the 
second,  so  that  a  space  is  left  between  the  two  through  which 
a  certain  amount  of  the  light  emitted  by  the  crater  can  escape. 

It  is  very  important  to  bear  well  in  mind  the  different 
meanings  that  attach  to  (1)  the  ordinary  polar  curve  of  candle- 
power,  (2)  the  Rousseau  figure  for  the  same  arc,  and  (3)  a 
curve  such  as  A  B  C  (Fig.  108).  Each  radius  vector  of  the 
polar  curve  is  proportional  to  the  whole  light  emitted  by  crater, 
arc  and  carbons,  in  one  direction  only  \  bat  the  area  of  this 
polar  curve  is  not  proportional  to  the  whole  light  emitted  by 
the  source,  as  is  frequently  erroneously  stated  (see  Appendix, 
p.  450).  It  is  the  area  of  the  Rousseau  figure  drawn  from  this 
polar  curve  that  is  proportional  to  the  whole  light  emitted  by 
the  source,  or  to  its  mean  spherical  candle  power.  Each 
Rousseau's  figure  of  crater  light  obtained  from  the  diagrams 
in  Fig.  103  represents  the  total  light  received  from  the  crater. 
In  the  curve  ABC  (Fig.  108)  each  ordinate  is  proportional  to 
the  whole  area  of  the  Rousseau  figure  of  crater  light,  for  the 
length  of  arc  represented  by  the  corresponding  abscissa.  Thus, 
the  curve  ABC  shows  the  connection  between  the  total  light 
received  from  the  crater  and  the  length  of  the  arc. 

Fig.  108  shows,  then,  without  a  doubt,  that  it  is  not  the 
light  received  from  the  crater  that  increases  to  a  maximum 
and  then  diminishes  again  as  the  arc  is  lengthened.  It 
remains  to  be  seen  whether  the  light  from  any  of  the  other 
sources — the  vapour,  the  white  spot,  or  the  glowing  carbon 
ends — has  a  maximum  value  for  a  given  length  of  arc.  First, 
as  regards  the  arc  vapour.  Both  the  length  and  the  cross- 
section  of  this  increase  as  the  arc  is  lengthened,  as  will  be 
seen  from  a  comparisonlof  Figs.  3  and  4,*  which  are  pictures  of 
the  arc  and  carbons  with  the  same  carbons  and  the  same 
current,  but  different  lengths  of  arc,  in  which  the  shape  of  the 
vapour  has  been  very  carefully  noted.  The  emitting  area  of 
the  vapour  increases,  therefore,  as  the  arc  is  lengthened ;  and, 
*  Between  pp,  6  and  7. 


TOTAL  LIGHT  &. LENGTH  OF  ARC  FROM  DIAGRAMS.  345 

since  we  may  take  it  that  its  intrinsic  brilliancy  is  fairly 
constant,  it  follows  that  the  total  light  emitted  by  the  vapour 
is  greater  the  longer  the  arc. 

The  white  spot  is,  I  find,  practically  constant  in  area  with  a 
constant  current,  and  as,  like  the  crater,  it  must  reveal  more 
of  its  light  the  longer  the  arc  is  made,  the  light  received  from 
this  also  must  increase  continuously  as  the  arc  is  lengthened. 

The  glowing  end  of  the  negative  carbon  gives  so  little  light 
that  we  may  certainly  neglect  it ;  but  that  of  the  positive 
carbon  must  be  taken  into  account.  The  length  of  this 
glowing  part  increases,  I  find,  as  the  arc  is  lengthened,  so 
that  if  we  assume  that  the  intrinsic  brilliancy  of  this  also 
is  fairly  constant  with  a  constant  current,  it  is  clear  that  the 
light  emitted  by  it  increases  as  the  arc  is  lengthened.  Thus 
the  light  from  each  of  the  minor  sources  in  the  arc  increases 
as  the  arc  is  lengthened,  with  a  constant  current.  If  we  take 
this  light  as  being  always  about  10  per  cent,  of  the  total  light 
received  from  the  crater,  the  curve  connecting  the  total  light 
received  from  the  arc  with  the  length  of  the  arc  will  be  of  the 
form  D  E  F  (Fig.  103).  From  this  curve  we  should  say  that 
the  total  light  received  from  the  arc  with  a  constant  current 
increases  very  rapidly  as  the  arc  is  first  lengthened  from  zero, 
and  continues  to  increase,  though  more  and  more  slowly,  till 
the  arc  is  infinitely  long.  Thus,  a  careful  examination  of  the 
light  received  from  all  the  sources  in  the  arc  fails  to  show  how 
there  can  be  a  maximum  amount  of  light  received  with  a 
given  length  of  arc.  Nevertheless,  there  can  be  no  doubt  that 
this  maximum  does  exist — experiment  has  proved  it  again  and 
again.  Such  able  experimenters  as  Prof.  Ayr  ton,  Prof.  Carhart 
and  M.  Blondel  have  all  come  to  the  same  conclusion. 

Why  Liyht-Length-of-Arc  Curves  deduced  from  Diagrams  Differ 
from  those  found  by  Experiment.  Absorption  of  Crater 
Light  by  Arc. 

In  seeking  an  explanation  of  this  curious  discrepancy 
between  two  sets  of  facts  connected  with  the  same  phenom- 
enon, we  must  turn  again  to  a  consideration  of  the  light 
emitted  by  the  crater.  Mr.  Trotter's  experiments,  while 
showing  that  the  light  of  the  crater  is  practically  uniform 
over  the  whole  surface,  give  no  indication  as  to  whether  the 


346  THE  ELECTRIC  ARC. 

light  received  from  the  crater  is  constant  for  all  currents  and 
lengths  of  arc  or  not.  It  is  plain  that  the  two  conditions — 
uniformity  over  the  whole  surface  and  constancy  for  all 
currents  and  lengths  of  arc — are  quite  distinct.  The  first 
might  easily  exist  without  the  second,  though  it  is  more 
difficult  to  conceive  of  the  second  without  the  first.  Each 
square  millimetre  of  a  10  ampere  2mm.  arc  might  easily  give 
the  light  of  100  candles,  while  each  of  a  100  ampere  10mm. 
arc  gave  200  candles,  but  it  is  difficult  to  believe  that  the 
average  amount  of  light  per  square  millimetre  emitted  by  two 
craters  of  very  different  areas  could  be  the  same,  without  the 
light  being  uniformly  distributed  over  the  whole  surface  of 
each.  There  is  a  third  condition,  however,  which  is  actually 
known  to  exist  in  the  arc,  and  which  necessitates  the  existence 
of  both  the  other  conditions,  viz.,  the  constancy  of  the 
temperature  of  the  crater  with  a  given  quality  of  carbon. 

Although  there  was  a  good  deal  of  vague  surmise  about  the 
volatilisation  of  carbon  at  the  crater  from  a  very  early  period 
in  the  history  of  the  arc,  it  was  Sir  William  Abney*  who,  in 
1881,  first  clearly  enunciated  the  theory  that  the  temperature 
of  the  crater  was  that  of  the  volatilisation  of  carbon,  and  must, 
therefore,  be  constant.  He  then  remarked,  "  Whether  the  crater 
be  one-eighth  or  half  an  inch  in  diameter,  the  brightness  remains 
constant,  being  apparently  due  to  the  temperature  at  which 
carbon  is  vaporised."  (The  italics  are  mine).  This  theory,  which 
marks  as  distinct  an  epoch  in  the  history  of  the  arc  as  Edlund's 
discovery  of  the  law  of  the  apparent  resistance,  has  been 
attributed  at  different  times  to  several  different  observers,  but 
Sir  William  Abney  was  undoubtedly  its  originator,  and,  in 
formulating  it,  he  made  a  very  great  advance  in  our  ideas 
concerning  the  physics  of  the  arc.  He  was  led  to  it  by  finding 
that  with  given  carbons  both  the  intensity  and  the  colour  of 
the  light  emitted  by  the  crater  appeared  to  be  quite  unaltered 
by  any  change  in  the  current  or  in  any  of  the  other  conditions 
of  the  arc. 

It  would,  perhaps,  be  more  correct,  as  several  observers  have 
suggested,  to  speak  of  the  sublimation  of  the  carbon  at  the 
surface  of  the  crater  than  of  its  volatilisation  \  for  there  is  no 

*  Phil.  Trans.,  1881,  Vol.  CLXXIL,  p.  890. 


CONSTANT  TEMPERATURE  OF  CRATER.  347 

evidence  to  prove  that  the  carbon  liquefies  before  volatilising. 
Indeed,  I  have  tried  pressing  the  two  ends  hard  together,  when 
a  large  current  was  flowing,  and  then  turning  off  the  current 
suddenly  before  separating  them,  without  finding  any  signs  of 
their  having  stuck  together,  or  even  moulded  one  another. 
On  the  other  hand,  a  small  carbon  placed  in  the  arc  near 
the  positive  pole  will  sometimes  bend  right  over,  so  that  the 
two  parts  make  a  very  distinct  angle  with  one  another,  and 
Prof.  Elihu  Thomson*  has  succeeded  in  bending  a  carbon  by 
merely  sending  a  current  through  it  large  enough  to  make 
it  white  hot. 

Prof.  Silvan  us  Thompson  has  expressed  an  opinion!  that  the 
temperature  of  the  crater  is  that  of  the  boiling  point  of  carbon. 
"  My  present  view  of  the  physical  state  of  the  arc  crater  is  that 
the  solid  carbon  below  is  covered  with  a  layer  or  film  of  liquid 
carbon  just  boiling  or  evaporating  off."  But  there  seems  to  be 
no  evidence  to  support  this  view,  for  even  if  the  thin  film 
of  liquid  carbon  exists,  which  is  very  doubtful,  it  probably 
evaporates  long  before  it  has  reached  the  boiling  point. 

The  question  has  been  attacked  from  another  side  by  various 
investigators,  of  whom  the  principal  are  Rossetti,J  and  Violle,§ 
who  found  the  temperature  constant  under  varying  conditions, 
Rossetti  estimating  it  at  3,900°C.,  and  Violle  at  3,500°. 
M.  Violle's  experiments  covered  a  very  wide  range  of  current — 
10  to  1,000  amperes — and  were  made  both  with  arcs  open  to 
the  air  and  with  arcs  enclosed  in  furnaces  ;  but  they  all  led  to 
the  same  conclusion,  viz.,  that  the  temperature  of  the  crater, 
with  given  carbons,  was  absolutely  independent  of  the  current 
and  of  the  P.D.  between  the  carbons.  Such  testimony  as  this 
must,  I  think,  negative  a  suggestion  made  by  M.  Blondel,  that 
the  diminution  in  the  light  emitted  by  the  arc,  after  it  had 
reached  a  certain  length,  was  caused  by  a  diminution  in  the 
intrinsic  brilliancy  of  the  crater  owing  to  cooling. 

Since  the  temperature  of  the  crater  with  given  carbons  is 
constant,  it  must  follow  that  its  intrinsic  brilliancy — the 

*  Electrical  Engineer  of  New  York,  March  27,  1891,  p.  322. 
t  The  Electrical  Review,  1895,  Vol.  XXXVII.,  pp.  571. 
J  La  Lumiere  Electriquc,  1879,  Vol.  I.,  p.  235. 

§  Comptes  Rcndus,  1892,  Vol.  CXV.,  p.  1,  273  ;  1894,  Vol.  CX1X.,  p.  949. 
Journal  dc  Physique,  1893,  Vol.  II..  p.  545. 


348  THE  ELECTRIC  ARC. 

amount  of  light  emitted  per  square  millimetre — must  also  be 
both  uniform  and  constant ;  for  a  greater  supply  of  energy  or 
a  smaller  withdrawal  through  cooling,  would  not  raise  the  tem- 
perature of  the  crater,  but  would  simply  cause  a  larger  quantity 
of  carbon  to  be  volatilised,  and  so  increase  the  area  or  depth  of 
the  crater,  or  both.  Similarly  an  increased  withdrawal  of 
energy,  or  a  diminution  in  the  supply  would  only  result  in  the 
formation  of  a  smaller  crater. 

Because,  however,  the  temperature  of  the  crater  is  constant, 
and  the  light  emitted  by  it  must  therefore  be  uniform  and  con- 
stant, it  by  no  means  follows  that  the  light  we  receive  from  it  is 
the  same.  There  may  be  some  reason  why  part  of  it  is  lost  in 
transmission,  and,  if  this  is  so,  the  evidence  gathered  from 
photometric  measurements  of  the  light  of  the  crater  will 
disagree  with  that  obtained  from  measurements  of  its 
temperature.  Such  a  disagreement  does  actually  exist,  for  not 
only,  as  I  have  mentioned  (p.  322),  is  the  light  received  from  the 
crater  not  always  uniform,  but  M.  Blondel*  has  shown  it  to 
be  more  than  doubtful  whether  it  is  constant  for  all  currents. 
While  pointing  out  that  such  experiments  must  be  received 
with  caution,  owing  to  the  way  in  which  the  crater  moves 
about,  M.  Blondel  mentioned,  in  the  admirable  series  of 
articles  from  which  we  have  already  gathered  so  much  informa- 
tion, that  the  maximum  brilliancy  of  the  crater  had  varied  in 
one  series  of  experiments  from  163  decimal  candles  per  square 
millimetre  with  a  current  of  5  amperes  to  210  candles  with 
one  of  25  amperes.  Thus,  although  the  intrinsic  brilliancy  of 
the  crater  may  be,  and  probably  is,  constant  in  the  main,  yet 
it  must  be  acknowledged  that  there  are  circumstances  under 
which  the  light  received  from  the  crater  is  neither  uniform 
over  its  whole  surface  nor  constant  for  all  currents. 

What  follows,  then  ?  That  the  emissivity  should  vary,  when 
the  substance  is  the  same  and  the  temperature  constant,  is 
inconceivable.  Before  it  reaches  the  eye,  however,  the  light 
of  the  crater  has  to  pass  through  a  region  filled  with  what  I 
have  hitherto  called  the  arc  vapour.  Our  eyes  tell  us  that 
this  vapour  must  consist  of  at  least  three  layers,  an  inner 
purple  kernel,  a  dark  envelope,  and  a  green  outer  aureole,  and 

*  L'Edairayc  Elcctri^uc,  1897,  Vol.  X.,  p.  500. 


SOLID  CARBON  PARTICLES  IN  THE  ARC.          349 

Prof.  Dewar  has  given  us  some  information  about  its  chemical 
constitution  ;  but  as  to  its  average  density,  or  the  density  of 
the  various  layers,  or  as  to  whether  these  densities  change 
when  the  current  and  length  of  arc  are  altered,  we  are  entirely 
ignorant. 

It  has  hitherto  been  taken  for  granted  that  this  complex 
vapour  (although  it  is  known  to  be  full  of  solid  carbon 
particles)  absorbs  none  of  the  light  of  the  crater,  or  a  quantity 
so  small  as  to  be  negligible.  But  what  if  the  amount  of  light 
absorbed,  though  very  small  when  the  quantity  of  vapour  to 
be  traversed  is  small,  as  it  is  when  the  arc  is  short,  becomes 
quite  noticeable  when  the  quantity  is  considerably  increased, 
as  it  is  by  lengthening  the  arc?  What  if  the  quantity 
absorbed  depends  not  only  on  the  amount  of  vapour,  but  also 
on  its  density,  its  constitution,  or  the  arrangement  of  its 
layers?  Then  the  light  received  from  the  crater,  far  from 
being  uniform  and  constant,  as  is  the  light  emitted  by  it,  will 
depend  upon  the  current,  the  length  of  the  arc,  the  motions 
of  the  various  layers — upon  everything,  in  fact,  that  can  cause 
a  change  in  the  density,  the  constitution,  the  number,  or  the 
relative  positions  of  the  layers  of  vapour.  Absorption  such 
as  this  would  account  for  all  the  anomalies  that  have  been 
observed  in  the  light  of  the  arc,  all  the  discrepancies  that 
appear  to  exist  between  the  evidence  gathered  from  direct 
measurements  of  the  light  of  the  crater  and  that  obtained  by 
measuring  its  temperature.  Let  us  see  wnat  evidence  there 
is  of  the  existence  of  such  absorbent  power  in  what  is  usually 
called  the  arc  vapour. 

In  1822  Silliman,*  the  editor  of  Sillimarfs  Journal  first 
observed  that  carbon  particles  were  shot  out  from  the  positive 
pole  of  an  arc  on  to  the  negative.  The  observation  has  since 
been  confirmed  by  experimenters  too  numerous  to  mention, 
but  Herzfeld  established  the  existence  of  solid  carbon  particles 
in  the  arc  beyond  doubt  by  the  beautiful  experiment  described 
on  page  85,  in  which  he  attracted  the  particles  out  of  the  arc 
on  to  a  highly  charged  insulated  plate  placed  near  it.  The 
existence  of  these  particles  in  the  arc  at  once  disposes  of  the 
theory  that  it  is  composed  of  pure  carbon  vapour,  or  even  of 

*  Sittiiflan'tt  Journal,  1822,  Vol.  V.,  p.  108, 


350  THE  ELECTRIC  ARC. 

such  vapour  mixed  with  gases,  and  places  what  I  shall  for  the 
future  call  the  arc  mist  in  the  same  category  as  the  flame  of  a 
candle,  which  is  also  known  to  contain  solid  carbon  particles. 

Having  arrived  at  this  conclusion,  it  occurred  to  me  that 
some  experiments  with  a  candle  flame  might  prove  useful  in 
suggesting  the  simplest  method  of  testing  the  light-absorbing 
power  of  the  arc  mist.  The  first  I  made  was  to  place  a  piece 
of  printed  paper  behind  the  flame  and  try  to  read  through  it. 
I  found  that  all  the  unshaded  part  of  the  flame  in  Fig.  109 
completely  hid  the  print,  but  that  I  could  see  through  the 


FIG.  109.— Photograph  of  Candle  Flame. 

remainder  as  through  a  mist,  the  most  transparent  part  being 
the  dark  region  all  round  the  wick.  When  the  paper  was 
placed  so  close  to  the  candle  that  it  was  in  danger  of  burning, 
it  could  be  read  through  any  part  of  the  flame,  but  when  it 
was  even  only  an  inch  away  from  the  flame  the  words  im- 
mediately behind  the  bright  part  were  completely  blotted  out. 
If,  however,  black  marks  were  made  on  a  piece  of  transparent 
paper,  and,  when  they  were  quite  invisible  through  the  flame, 
another  candle  was  brought  up  behind  the  paper,  they 


OPACITY  OF  CANDLE  FLAME.  351 

reappeared  as  soon  as  the  light  from  the  second  flame  shone 
through  the  paper.  If,  also,  the  light  from  an  incandescent 
gas  burner  shone  full  on  the  opaque  printed  paper  from  the 
front,  the  words  on  it  could  be  easily  read  through  the  flame 
of  a  candle  placed  even  as  much  as  six  inches  away.  Thus, 
if  the  paper  were  only  brightly  enough  lighted,  either  from 
behind  or  in  front,  the  words  on  it  could  be  easily  read 
through  the  candle  flame.  This  proved  that  it  was  want  of 
light,  and  not  excess  of  light,  i.e.,  dazzling,  that  prevented  the 
paper  from  being  read,  for  in  the  latter  case  throwing  more 
light  on  it  would  have  increased  the  difficulty. 

On  the  other  hand,  the  want  of  light  was  not  necessarily 
all,  or  even  principally  due  to  absorption.  Some  part  of  the 
loss — probably  a  large  part — was  due  to  reflection,  internal 
reflection  among  the  solid  particles,  and  reflection  back  on  to 
the  paper.  A  very  pretty  proof  of  the  latter  was  discovered 
by  Mr.  Burch  in  1885.*  Concentrating  a  strong  beam  of 
sunlight  on  the  flame  of  a  candle  by  means  of  a  lens,  he  found 
that  enough  of  the  light  was  reflected  by  the  flame  to  enable 
him  to  analyse  it  in  a  spectroscope  and  to  prove  that  it  was 
indeed  sunlight  and  not  candle  light  that  was  analysed.  He 
also  found  that  the  reflected  light  was  polarised  in  directions  at 
right  angles  to  the  incident  rays,  showing  that  the  reflection 
was  due  to  minute  solid  particles  in  the  flame. 

Sir  George  Stokes, t  without  having  heard  of  Mr.  Burch's 
experiments,  re-discovered  the  power  of  a  candle  flame  to 
reflect  sunlight  later.  He  sent  a  highly  condensed  beam  of 
sunlight  through  the  flame  of  a  candle,  and  noticed  two  bright 
spots  of  white  light  at  the  parts  of  the  surface  of  the  flame 
where  the  cone  of  rays  entered  and  left  it.  He  could  not  trace 
the  passage  of  the  beam  through  the  flame,  and  hence  concluded 
that  the  layer  of  solid  particles  was  extremely  thin  and  situated 
only  at  the  surface.  I  have  tried  the  same  experiment,  but  it 
seemed  to  me  that  in  some  parts  of  the  flame  a  faint  haze 
joined  the  two  bright  splashes  of  blue  light.  It  is  extremely 
difficult  to  be  sure  of  this,  however,  because  the  faintest  flicker 
of  the  flame  causes  a  ring  of  bluish  light  to  encircle  it,  instead 


*  Nature,  1885,  Vol.  XXXL,  p.  272. 
t  Nature,  1891,  Vol.  XLV.,  p.  133. 


352  THE  ELECTRIC  AEC. 

of  the  two  bright  spots  only,  and  the  apparent  faint  haze  may 
be  only  the  inner  coating  of  the  farther  side  of  this  ring. 

Owing  to  dark  weather  I  was  unable  to  send  a  beam  of 
sunlight  on  to  the  arc,  but  I  tried  whether  objects  were  hidden 
by  the  arc  mist  as  they  are  by  candle  flames.  I  looked  through 
a  slit  that  protected  the  eyes  from  all  light  but  that  of  the 
mist,  which  was  much  brighter  than  might  have  been  expected> 
but  not  so  strong  as  to  completely  dazzle  me.  The  result  was 
just  what  I  anticipated,  as  regards  the  purple  core — it  behaved 
exactly  like  the  candle  flame  in  blotting  out  printed  letters 
that  were  looked  at  through  it.  The  green  aureole,  however, 
was  much  more  transparent,  allowing  the  letters  to  be  read 
easily  through  it.  Thus,  in  this  one  way  at  least,  the  arc 
behaves  to  light  transmitted  through  it  exactly  as  the  flame 
of  a  candle  does. 

The  Shadow  of  the  Arc. 

The  success  of  this  experiment  made  it  seem  worth  while  to 
try  whether  the  arc,  like  the  candle,  would  cast  a  shadow.  To 
do  this  I  thought  at  first  of  sending  the  light  of  one  arc,  through 
another,  on  to  a  screen  from  which  all  the  direct  light  from  the 
crater  and  carbons  of  the  second  arc  was  cut  off,  so  that  the 
shadow,  if  there  were  one,  might  be  as  sharp  as  possible. 
Mr.  Mather,  however,  who  very  kindly  superintended  the  first 
experiments  for  me,  contrived  a  far  simpler  and  better  method 
involving  the  use  of  one  arc  only.  The  arrangement  is  shown 
in  section  in  Fig.  110. 

A  was  a  plane  mirror  placed  so  as  to  receive  a  large  amount 
of  the  light  from  the  crater  and  to  reflect  it  on  to  a  screen 
of  white  cartridge  paper  B  C.  The  screen  was  placed  high 
above  the  tip  of  the  positive  carbon,  and  was  tilted  so  that  it 
should  catch  none  of  the  direct  light  from  the  crater,  and 
as  little  as  possible  from  the  carbons.  The  mirror  A  was 
wider  than  the  arc,  so  that  only  a  part  of  the  light  it  reflected 
went  back  through  the  arc,  and  a  part  on  either  side  went 
straight  on  to  the  screen.  Thus,  if  any  of  the  light  reflected 
by  the  mirror  were  absorbed  in  the  arc,  or  even  if  it  were 
simply  reflected  back  again  by  the  arc  mist  on  to  the  mirror, 
a  shadow  of  the  arc  would  appear  on  the  screen.  This  is  just 
what  happened.  Deep  shadows  of  the  carbons  appeared,  with 


ARC  SHADOW. 


353 


a  fainter  shadow  between. 
This  faint  shadow  deepened 
when  the  arc  was  lengthened. 

This  seemed,  at  first,  con- 
clusive proof  that  a  compara- 
tively large  part  of  the  light 
sent  through  the  arc  was 
either  absorbed  by  it  or  re- 
flected back  on  to  the  mirror. 
The  affair  was  not  so  simple, 
however.  Mr.  Mather  noticed 
a  rim  of  light  round  the  shadow 
of  the  arc,  which  was  brighter 
than  any  other  part  of  the 
screen.  He  pointed  out  that 
this  could  only  be  caused  by 
the  light  sent  through  the  arc 
mist  being  refracted,  on  ac- 
count of  the  difference  of 
density  between  the  mist  and 
the  surrounding  air.  The  arc, 
in  fact,  acts  as  a  lens  towards 
light  sent  through  it.  Now, 
a  concave  lens  which  is  denser 
than  air  throws  a  shadow  that 
has  a  rim  of  light  round  it — 
just  such  a  shadow  as  the  arc 
throws.  But  the  arc  is  dis- 
tinctly convex,  and  the  peculiar 
light-rimmed  shadow  that  it 
throws  proves,  therefore,  that 
it  is  less  dense  than  the  sur- 
rounding air.  It  acts,  in  fact, 
as  a  double-convex  negative 
lens,  one  having  a  refractive 
index  less  than  unity. 

This  lens  effect  is  not  con- 
fined to  the  arc ;  it  is  even 
stronger  in  candle  and  gas 
flames,  as  I  found  by  sending 


354  THE  ELECTRIC  ARC. 

the  light  of  the  arc  through  them.  An  account  of  some  inter- 
esting results  obtained  in  this  way  will  be  found  in  the 
Appendix  (p.  452). 

If  the  arc  shadow  is  produced  simply  by  refraction,  it  does 
not,  of  course,  necessarily  involve  any  loss  of  crater  light ;  the 
distribution  only  may  be  altered,  and  not  the  quantity  that  is 
received  outside  the  arc.  It  is  possible,  however,  that  even  a 
re-distribution  of  the  crater  light  might  involve  a  certain 
amount  of  loss  or  gain  owing  to  the  peculiar  way  in  which  the 
arc  lies  between  the  carbons,  for  the  part  of  the  vapour  lens 
which  is  near  the  negative  carbon  is  so  shaped  that  it  must 
bend  back  into  that  carbon  many  rays  from  the  crater  that 
would  otherwise  pass  it,  and  bend  others  away  from  it  that 
would  otherwise  enter  it. 

It  is  clearly  only  the  refraction  of  rays  whose  paths, 
without  it,  would  lie  within  a  certain  distance  from  the 
surface  of  the  negative  carbon,  both  internally  and  externally, 
that  can  have  any  effect  on  the  total  amount  of  crater  light 
received  outside  the  arc ;  and  this  distance  must  be  deter- 
mined by  the  refractive  index  of  the  mist.  What  this  is, 
under  any  given  circumstances,  and  whether  it  alters  with  the 
current  and  the  length  of  the  arc,  is  not  known.  Indeed,  the 
whole  question  of  the  refraction  is  fraught  with  difficulties 
and  surprises.  Who  could  have  foretold,  for  instance,  that  all 
the  three  parts  of  the  arc,  the  purple  core,  the  shadow,  and 
the  green  envelope  would  have  the  same  refractive  index? 
Yet  they  must  have,  for  the  shadow  they  throw  on  the  screen 
is  apparently  of  uniform  depth,  and  surrounded  by  a  single 
rim  of  light,  and  is  of  a  size  and  shape  which  show  that  it 
belongs  to  all  three  portions. 

Again,  the  refractive  power  of  the  mist  must  depend  on  its 
density  relatively  to  the  surrounding  air,  and  that  again  on 
the  relative  temperatures  of  the  two.  Now  it  is  true  that 
M.  Violle*  found  the  temperature  of  the  arc  higher  than  that 
of  the  crater,  but  this  was  with  an  arc  enclosed  in  a  furnace. 
Such  an  enclosure  alters  all  the  conditions  of  temperature,  and 
results  thus  obtained  can  give  no  clue  to  the  relative 
temperatures  of  the  arc  and  carbons  in  the  open  air.  No  very 

*  Journal  de  Physique,  1893,  3rd  Series,  Vol.  II.,  p.  545.  Comptes  Rend  us, 
1894,  Vol.  CXIX.,  p.  949. 


ARC  VAPOUR  AND  MIST.  355 

definite  experiments  have  yet  been  made  on  this  point  with 
the  open  arc,  but  the  following  considerations  point  to 
the  conclusion  that  the  average  temperature  of  the  arc  mist 
must  be  lower  with  a  long  arc  than  with  a  short  one,  when  the 
same  current  is  flowing  in  both. 

Since  Sir  William  Abney  first  announced  that  the  crater 
was  at  the  temperature  of  volatilisation  of  carbon  it  has  never 
been  doubted  that  the  stuff  of  which  the  arc  was  composed 
consisted  chiefly  of  the  vapour  thus  volatilised.  But  how  can 
this  be  so  ?  That  it  leaves  the  positive  carbon  as  vapour  there 
can  be  but  little  doubt,  but  that  by  the  cooling  action  of  the  air 
around  it  its  temperature  must  be  lowered,  and  that  it  must 
therefore  condense,  at  a  very  short  distance  from  the  crater, 
there  can  be  as  little  doubt.  My  own  belief  is  that  the 
vapour,  in  leaving  the  crater,  acts  just  as  steam  does  when 
issuing  from  the  mouth  of  a  kettle.  Through  a  distance  small 
enough  for  its  temperature  to  continue  unaltered  it  still 
remains  vapour;  at  greater  distances  it  is  condensed  into 
carbon  fog  or  mist.  The  true  vapour  is  probably  invisible, 
just  as  water  vapour  is  (the  space  that  is  always  seen  between 
the  arc  and  the  crater  confirms  this  view),  but  the  mist  is 
visible.  The  resistance  of  true  vapour  is  very  great,  and 
consequently  the  resistance  of  the  thin  layer  of  vapour  that 
lies  over  the  crater  is  so  great  compared  with  that  of  the 
remainder  of  the  arc  that  it  is  usually  supposed  not  to  be  a 
resistance  at  all  but  a  back  E.M.F.  The  heat  evolved  by  the 
passage  of  the  current  through  this  great  resistance  is 
sufficient  to  volatilise  the  surface  of  a  part  of  the  positive 
carbon,  and  thus  to  keep  up  the  supply  of  vapour.  The  part 
of  the  surface  that  is  thus  volatilised  becomes  hollow  with 
short  arcs  in  the  way  explained  in  Chapter  XII.  (p.  393),  and 
thus  the  crater  is  formed  by  the  action  of  heat  supplied  to  it 
by  the  thin  layer  of  vapour  that  spreads  over  its  surface. 

According  to  this  theory  of  the  arc,  the  temperature  of  any 
horizontal  section  of  the  mist  must  depend  upon  (1)  the 
temperature  at  which  it  left  the  crater,  (2)  the  constant  supply 
of  heat  conveyed  to  it,  by  radiation  from  the  crater,  (3)  the 
heat  evolved  by  the  passage  of  the  current  through  it,  and 
(4)  the  cooling  effect  of  the  surrounding  air.  If  we  take  a 
section  at,  say,  1  mm.  from  the  tip  of  the  negative  carbon,  the 

AA2 


356  THE  ELECTRIC  ARC. 

supply  of  heat  received  from  the  crater  will  be  less  the 
longer  the  arc,  and  the  cooling  effect  of  the  surrounding  air 
will  be  greater  the  longer  the  arc.  On  both  accounts  the 
average  temperature  of  the  mist  must  be  lowered  by  lengthen- 
ing the  arc,  and  consequently  its  average  density  must  be 
increased. 

The  reasons  for  considering  that  the  arc  mist  absorbs  an 
appreciable  amount  of  the  light  emitted  by  the  crater  are, 
then — 

(1)  That  this  mist  shares  with  candle  and  gas  flames  the 
power  to  hide  anything  placed  behind  it,  as  if  it  were  opaque. 

(2)  The  acknowledged  and  proved  existence  of  solid  particles 
in  it. 

(3)  Its  casting  a  shadow,  which  can  hardly  be  due  merely  to 
refraction. 

Change  of  Colour  of  Arc  Light  as  the  Arc  is  Lengthened. 

The  strongest  proof  that  the  arc,  when  it  is  long,  absorbs 
quite  a  considerable  portion  of  the  light  of  the  crater  is,  how- 
ever, this  : — Sir  W.  Abney  has  shown  *  that  crater  light  is 
very  like  sunlight,  but  has  a  slight  excess  of  orange  and  green 
rays  and  a  slight  deficiency  of  blue.  He  measured  the  light 
in  such  a  direction  that  he  was,  as  far  as  possible,  getting  rays 
from  the  crater  only,  that  is  to  say,  in  a  direction  in  which 
as  little  of  the  arc  as  possible  was  interposed  between  the 
spectroscope  and  the  crater.  The  crater  light  seen  through  a 
small  quantity  of  mist,  then,  is  yellower  than  sunlight.  But 
this  very  light,  when  it  has  penetrated  through  the  mist  of  a 
long  arc,  is  bright  purple  in  colour,  as  may  be  deduced  from 
the  colour  of  the  opalescent  globes  surrounding  arc  lamps, 
when  the  arc  is  long.  And  this  colour  has  nothing  to  do  with 
the  fact  that  our  being  accustomed  to  the  yellow  light  of  gas 
and  incandescent  lamps  after  dark  makes  a  pure  white  light 
appear  blue,  for  even  in  broad  daylight  the  globes  surrounding 
arc  lamps,  in  which  the  arc  is  long,  appear  bright  purple. 
Indeed,  I  have  seen  the  inside  of  a  screen  surrounding  a  long 
arc  flooded  with  purple  light  as  if  lighted  by  a  stained  glass 
window,  and  retaining  this  colour  even  when  daylight  was  let 

*  fieport  on  the  Action  of   Light  on  Water  Colours,  c.  5,453,  1888, 
pp.  23  and  69. 


ABSORPTION  OF  LIGHT  IN  THE  ARC.  357 

in  on  it.  There  can,  therefore,  be  no  doubt  that  the  light 
of  the  crater  becomes  tinged  with  violet  or  purple  as  it  passes 
through  the  arc,  and  that  the  tint  deepens  as  the  arc 
lengthens.  If  light  became  coloured  in  this  way  by  being 
passed  through  coloured  glass,  we  should  say  it  was  because 
the  glass  absorbed  rays  of  certain  colours  and  allowed  other 
rays  to  pass.  Why,  then,  should  not  this  explanation  apply 
to  the  arc  mist  ? 

What  probably  happens  is  this.  The  arc,  except  a  thin 
layer  quite  close  to  the  crater,  consists  of  a  mist  of  solid  carbon 
particles,  which  are  continually  forming  and  falling,  surrounded 
by  burning  gases.  The  vapour  and  gases  must,  of  course,  absorb 
a  minute — possibly  an  inappreciable — portion  of  the  light  that 
issues  from  the  crater.  If  this  were  all,  there  would  probably 
be  no  maximum  of  light  with  a  given  length  of  arc ;  but  the 
solid  carbon  particles  have  to  be  reckoned  with.  If  the  light 
simply  passed  through  each  of  these  that  it  encountered,  and 
suffered  only  the  small  amount  of  absorption  that  would 
naturally  take  place,  the  whole  quantity  of  light  absorbed 
might  still  be  too  small  to  notice.  But  a  ray  of  light  en- 
countering a  white  hot  particle  is  not  only  refracted — some  of 
it  is  reflected,  so  that  each  ray  may  be  reflected  from  particle 
to  particle,  and  so  may  traverse  the  mist  hundreds  of  times 
before  it  finally  emerges.  At  each  reflection  and  refraction 
part  of  the  light  that  the  particle  is  capable  of  absorbing  is 
absorbed,  and  a  ray  that  has  suffered  much  internal  reflection 
must  emerge  in  a  very  different  state  from  that  in  which  it 
left  the  crater. 

Suppose,  now,  that  the  carbon  particles  were  capable  of 
absorbing  the  orange  light  and  a  certain  amount  of  the  green, 
but  allowed  all  the  violet  light  to  pass.  Then,  after  each 
successive  reflection  or  refraction,  the  light  would  become 
more  violet,  and  that  which  had  encountered  many  particles 
would  be  entirely  violet.  No  incandescent  gases  alone  give  a 
dazzlingly  brilliant  light,  so  that  when  one  looked  at  the 
arc  mist  alone,  screening  off  the  whole  direct  light  from  both 
carbons,  the  part  of  the  crater  light  that  was  transmitted 
to  the  eye  from  the  solid  particles  would  entirely  swamp  the 
feeble  light  emitted  by  the  gases,  and  one  would  only  perceive 
a  brilliant  violet  or  purple  light.  This  would  account  for 


358 


THE  ELECT1UC  AHG. 


the  light  of  the  arc  alone  being  so  much  more  brilliant  than 
one  would  expect. 

A  very  simple  experiment  will  suffice  to  show  that  the  light 
emitted  by  the  arc  mist  is  violet,  while  that  emitted  by  the 
crater  and  the  white  hot  spot  on  the  negative  carbon  is  white. 
If  a  thin  metal  plate,  containing  a  horizontal  slit  a  (Fig.  Ill) 
about  jV0-  in  width,  be  held  vertically  near  an  arc  so  that  the 
slit  is  about  equidistant  from  the  ends  of  the  two  carbons, 
and  if  the  light  from  the  arc  that  passes  through  the  slit  be 
received  upon  a  vertical  white  screen  cd,  a  foot  or  two  away, 
this  light  will  form  three  horizontal  bands  on  the  screen,  the 
upper  and  lower  ones  being  white  and  the  middle  one  of  a 


White  Negative 
Light. 

Violet 
Mist  Light. 

White 
Crater  Light 


FIG.  111. — Light  from  Crater,  Mist,  and  White  Spot  passing  through  a 
Narrow  Slit  on  to  a  White  Screen. 


bright  violet.  The  slit  is,  of  course,  simply  a  pinhole  horizon- 
tally elongated,  so  that  the  upper  white  light  must  proceed 
from  the  negative  carbon,  as  indicated  by  the  lines  in  Fig.  Ill, 
the  lower  from  the  crater,  and  the  middle  violet  band  must 
be  lighted  by  the  arc  mist. 

A  still  simpler  experiment  is  that  of  shading  the  upper 
carbon  and  part  of  the  arc  with  any  opaque  body,  one's  hand, 
for  instance.  The  shadow  on  the  screen  will  then  be  found 
to  be  edged  with  a  broad  band  of  reddish  violet  light,  this 
band  being  the  portion  of  the  screen  that  is  illuminated  by 
the  mist  and  the  negative  carbon  alone  (the  red-hot  part  of 


VIOLET  SHADOW  CAST  BY  THE  ARC. 


359 


this  carbon  gives  the  rosy  tinge).  Below  the  band  is  the  part 
illuminated  by  all  three  sources — crater,  mist  and  white  hot 
spot — and  this  naturally  looks  quite  white  when  contrasted 
with  the  violet  band.  A  diagrammatic  illustration  of  this 
experiment  is  given  in  Fig.  112;  ab  is  a  metal  plate,  cd  the 
white  screen  on  which  the  light  falls.  The  portion  above  is 
entirely  in  shadow,  that  between  c  and  d  is  lighted  by  mist 
and  negative  carbon  alone,  and  that  below  d  is  illuminated  by 
the  crater  as  well  as  by  these. 

This  absorption  by  internal  reflection  would  also  explain 
a  curious  anomaly  pointed  out  by  Mr.  Swinburne  in  the 
discussion  on  the  Paper  by  Mr.  Trotter,*  already  quoted. 


Shadow. 


Violet 
Light. 


White 
Light. 


FIG.  112.— Band  of  Violet  Light  bordering  the  Shadow  of  a  Metal  Plate 
which  is  cutting  off  the  Lighfc  from  the  Crater  of  an  Arc. 

Mr.  Trotter  exhibited  the  curves,  published  by  Sir  W.  Abney, 
which  showed  that  crater  light  only  differed  from  sunlight 
in  having  a  slight  excess  of  orange  and  green  rays  and  a 
slight  deficiency  of  blue  rays.  Mr.  Swinburne  pointed  out 
that  as  crater  light  and  sunlight  were  so  very  nearly  of  the 
same  colour,  the  sun  and  the  crater  must  also  be  nearly  of 
the  same  temperature ;  but  that,  as  the  sun  gave  above 
ten  times  as  much  light  per  square  millimetre  as  the  crater, 
the  emissivity  of  the  sun  must  be  ten  times  as  great  as 
that  of  the  crater,  which  was  incredible.  This  objection 

*  Journal  of  the  Institution  of  Electrical  Engineers,  1892,  Vol.  XXI. > 
p.  381. 


360  THE  ELEGTEIG  ARG. 

is  perfectly  valid  if  sunlight  and  the  light  emitted  by  the 
crater  are  really  so  nearly  of  the  same  colour.  But  Sir  W 
Abney  was  only  able  to  measure  the  light  received  from  the 
crater  after  it  had  passed  through  a  certain  quantity  of  the  mist, 
for  it  is  impossible  for  the  crater  light  to  get  out  without  pass- 
ing through  some  mist.  Suppose,  then,  that  the  light  emitted 
by  the  crater  were  very  much  yellower  than  the  sun,  but  that 
even  in  passing  through  this  small  quantity  of  mist  it  was 
robbed  of  a  considerable  portion  of  its  orange  and  green  rays  : 
then  when  it  reached  the  photometer  its  colour  would  by  this 
means  have  been  brought  much  nearer  to  that  of  sunlight  than 
it  had  been  when  it  left  the  crater;  it  would  have  been  rendered 
bluer  in  the  course  of  transmission,  and  would  appear,  there- 
fore, to  have  been  emitted  by  a  surface  of  much  higher 
temperature  than  the  surface  of  the  crater  actually  is.  Thus, 
if  the  mist  does  really  absorb  any  considerable  portion  of  the 
orange  and  green  rays,  Mr.  Swinburne's  objection  no  longer 
holds,  for  the  crater  light  is  probably  far  yellower  when  it  is 
emitted  than  when  it  is  measured. 

Now  take  the  effect  of  lengthening  the  arc  on  the  light 
emitted  by  the  crater.  The  arc  mist  would,  on  the  whole,  be 
cooler,  there  would  be  more  solid  particles,  and  each  ray  would, 
therefore,  run  a  greater  chance  of  encountering  one  or  more  of 
these  particles  before  emerging.  Thus  more  of  the  light  on 
the  whole  would  be  absorbed,  and  more  of  the  rays  would  have 
been  robbed  of  all  the  light  the  particles  were  capable  of 
absorbing  before  emerging,  so  that  the  light  would,  on  the 
whole,  be  more  violet  than  with  a  shorter  arc — as  it  actually  is. 

Absorption  of  Crater  Light  in  Successive  layers  of  the  Arc. 

So  far,  all  the  evidence  appears  to  be  in  favour  of  the  theory 
of  the  absorption  of  crater  light  in  the  carbon  mist,  but  it  still 
remains  to  be  seen  how  far  this  theory  will  account  for  the 
curious  phenomenon  that  started  the  inquiry — the  existence 
of  maximum  points  in  the  curves  connecting  the  total  light 
of  the  arc  with  its  length,  when  the  current  is  constant.  For 
this  purpose  we  will  take  the  curve  constructed  in  Fig.  108, 
connecting  the  whole  light  emitted  by  the  crater,  arc,  and 
carbons,  with  the  length  of  the  arc,  with  a  current  of 
20  amperes,  and  see  whether,  by  subtracting  a  fraction  of  the 


ABSORPTION  OF  CRATER  LIGHT  BY  THE  ARC.     361 

crater  light  of  the  same  magnitude  as  the  light  absorbed 
would  probably  be,  from  the  light  of  each  length  of  arc,  we 
obtain  a  curve  resembling  those  found  by  Profs.  Ayrton  and 
Blondel  from  actual  measurement  of  the  light. 

We  must  first  find  what  fraction  of  the  crater  light  would 
be  absorbed  in  any  given  length  of  arc  when  it  is  assumed 
that  some  fixed  fraction  of  the  whole  light  that  enters  any 
given  layer  of  mist  is  absorbed  in  that  layer.  Let  us  divide 
the  arc  mist  into  layers  of  the  kind  shown  by  the  dotted  lines 
in  Fig.  113,  each  half  a  millimetre  thick  at  its  thickest  part, 
and  let  us  suppose  that  each  layer  absorbs  one  nth  part  of  the 
crater  light  that  enters  it.  The  law  is,  of  course,  really  far 


FIG.  113.— Arc  with  Mist  divided  into  Layers  of  Equal  Thickness. 


more  complicated  than  this,  but  we  cannot  hope,  in  any  case, 
to  obtain  more  than  a  very  rough  estimate  of  the  light  ab- 
sorbed without  more  exact  data  than  are  obtainable  at  present. 
The  amount  of  light  that  escapes  from  the  first  layer  will  be 

L  -  -    or  —  —  L.     After  it  has  passed  through  the  second  layer 

n  n 

the  quantity  of  light  will  be 

n  -  1  T      n  -  1  T         (n  -  \\  2r 
L  -        -  L,  or  (        -  )  L, 
n  n2  \    n    J 

and  after  passing  through  the  Zth  layer  it  will  be 

c  ;')'•• 


362 


THE  ELECTKIC  ARC. 


The  quantity  of  crater  light  that  escapes  from  an  arc  of  I  mm. 
will  therefore  be 


Now  we  have  L  for  each  length  of  arc  corresponding  with  a 
point  on  the  curve  ABC  (Fig.  108).  Let  us  take  w  =  40, 
which  is  equivalent  to  saying  that  two  and  a-half  per  cent,  of 
the  whole  light  that  enters  each  half  millimetre  layer  of  the 
arc  mist  is  absorbed  by  that  layer.  Table  LI.  gives  the  total 
crater  light  before  absorption,  the  same  after  absorption,  and 
this  latter  crater  light  plus  10  per  cent.,  to  allow  for  the  light 
emitted  by  the  other  sources,  for  each  length  of  arc. 

Table  LI.  —  Crater  Light  that  would  Escape  Without  and  With 
Absorption,  and  Total  Light  Emitted  by  Arc  if  there  is 
Absorption,  in  Arcs  used  for  Curve  A  B  C,  Fig.  108. 


Length  of  Arc 
in  mm. 

I 

CW?thoLufht           Crater  Light 
Action.        With  Absorption 

Crater  Light  With 
Absorption,  plus 
10    per    cent,    of 
same. 

0-5 
1-1 
'2-0 
3-2 
6'6 

7-8 
912 
10-12 
11-76 
14-15 

7-6 
8-63 
9-14 
9-90 
10-13 

8-36 
9-49 
10-05 
10-89 
1114 

Light-Length-of-Arc  Curves  drawn  from  Diagrams,  allowing  for 
Absorption  of  Crater  Light  in  Arc. 

If,  now,  a  curve  be  drawn  connecting  the  total  light  emitted 
by  the  arc  (column  4,  Table  LI.)  with  its  length  (column  1)  this 
curve  should,  if  my  assumption  concerning  the  absorption  of  the 
crater  light  is  correct,  resemble  the  curves  in  Figs.  97, 98, 101  and 
102.  In  Fig.  114  this  curve  is  given,  and  it  will  be  seen  that 
it  resembles,  in  every  particular,  the  curves  drawn  from  actual 
measurements  of  the  light  in  Figs.  99  and  100,  even  to  having 
a  dip  between  1mm.  and  3mm.,  which  is  practically  imper- 
ceptible in  D  E  F  (Fig.  108),  which  is  the  curve  that  would 
connect  the  total  light  emitted  by  the  arc  with  its  length  if 
there  were  no  absorption  of  the  crater  light.  The  hollow  is 
not  so  deep  as  to  form  an  actual  minimum  point,  because 
20  amperes  is  not  a  large  enough  current  with  carbons  of 


LIGHT  CURVES  DEDUCED  FROM  DIAGRAMS.      363 


18mm.  and  15mm.  for  the  negative  carbon  to  be  very  pointed, 
even  with  a  short  arc. 

The  real  interest  of  Fig.  1H,  however,  lies  in  the  fact  that 
the  curve  has  a  maximum  point  somewhere  between  3mm.  and 


\ 


6mm.  For  this  shows  that  if  there  is  an  absorption  of  any- 
thing like  2 \  per  cent,  of  the  crater  light  in  every  half  millimetre 
of  the  arc  mist,  the  total  light  emitted  by  the  arc,  with  18/1 5mm. 


364  THE  ELECTRIC  ARC. 

carbons  and  a  current  of  20  amperes,  will  rise  to  a  maximum 
with  an  arc  of  about  4'5mm,  and  then  diminish.  That  is  to 
say,  on  the  assumption  of  this  very  possible  rough  law  of 
absorption  in  the  mist,  the  light  curve  obtained  from  measure- 
ments of  diagrams  of  arcs  and  carbons  resembles  that  obtained 
by  actual  measurement  of  the  light.  This  completes  the  chain 
of  evidence  in  favour  of  an  appreciable  portion  of  the  crater 
light  being  absorbed  in  the  arc  mist ;  and,  while  each  separate 
piece  of  evidence  may  possibly  be  open  to  some  other  interpreta- 
tion than  that  given  to  it,  yet  the  whole  together  seems  to 
afford  an  overwhelming  presumption  in  favour  of  the  theory. 

Effect  of  Variation  of  Current  on  Total  Light  emitted  by  Arc. 

Having  examined  the  effect  on  the  total  light  received 
from  the  arc  of  varying  its  length,  while  the  current  is  kept 
constant,  the  next  question  to  consider  is  how  the  light  is 
affected  by  varying  the  current.  This  question  may  be 
approached  in  two  ways :  either  the  length  of  the  arc  or 
the  P.D.  between  the  carbons  may  be  kept  constant  while 
the  current  is  varied.  Prof.  Ayrton  chose  the  first  way, 
M,  Blondel  the  second.  The  first  has  more  scientific,  the 
second  more  commercial  interest ;  for,  while  the  amount  of 
crater  light  that  can  get  past  the  negative  carbon  and  the 
quantity  that  is  absorbed  by  the  arc  mist,  both  depend 
immediately  on  the  length  of  the  arc,  the  makers  of  arc 
lamps  do  not  concern  themselves  with  the  exact  length  of  the 
arc,  but  only  with  the  current  and  the  P.D.  between  the 
carbons,  or  rather,  between  the  terminals  of  the  lamp. 

The  diagrams  in  Fig.  115  show  how  the  shapes  of  the 
carbons  and  arc  change  as  the  current  is  increased,  while  the 
length  of  the  arc  remains  constant.  For  the  upper  row 
currents  of  10,  25  and  35  amperes  were  used  with  a  4mm.  arc  ; 
and,  for  the  lower,  the  currents  were  6,  20,  and  30  amperes,  and 
the  length  of  the  arc  was  Of5mm.  The  first  thing  that  strikes 
the  attention  in  these  diagrams  is  the  way  in  which  the  crater 
enlarges  as  the  current  is  increased.  For  instance,  in  the 
upper  row  the  diameters  of  the  craters  for  10  and  25  amperes 
were  5'4mm.  and  8'4mm.  and  the  areas  of  their  mouths  were, 
therefore,  22*9  and  55 '4  sq.  mm.,  i.e.,  the  light-giving  surface 
of  the  25-ampere  crater  was  more  than  double  that  of  the 


LIGHT  EMITTED  WITH  VARIOUS  CURRENTS.      365 

10-ampere  crater.  Thus  the  light  received  in  each  direction 
from  which  the  crater  could  be  seen  must  have  been  more  than 
doubled  by  increasing  the  current  from  10  to  25  amperes.  It 
does  not  necessarily  follow,  however,  that  the  total  amount 


FIG.  115. — Effect  of  Variation  of  Current  on  Shapes  of  Carbons. 

of  light  received  outside  the  arc  was  thus  largely  increased, 
for  the  angles  through  which  the  whole  crater  could  be  seen 
and  through  which  any  part  of  it  could  be  seen  might  be 
proportionately  diminished.  There  is  no  such  diminution, 


366 


THE  ELECTRIC  ARC. 


however,  as  will  be  seen  from  a  comparison  of  the  angles  ABC 
and  E  B  D  for  the  three  currents  in  each  row.     In  all  cases, 

(Ayrton.) 


mm. 


1  mm. 


30 


35 


5  10  15  20  25 

Current  in  Amperes. 
FIG.  116.—  Curves  connecting  Mean  Spherical  Candle-power  with  Current  for 

Constant  Lengths  of  Arc  of  1mm.  and  4mm. 
Carbons  :  Positive  13min.  cored  ;  negative,  llmm.  solid, 


TOTAL  LIGHT  AND  CURRENT. 


367 


therefore,  if  none  of  the  crater  light  were  absorbed  in  the 
arc  mist,  the  light  received  from  the  crater,  and  therefore 
the  whole  light  received  from  all  sources  would  increase  as 
the  current  was  increased  with  a  constant  length  of  arc. 

(Blonde!.) 


45,000 


40,000 


35,000 


30,000 


20,000 


15,000 


10.000 


5,000 


10 


25 


30 


35 


15  20 

Current  in  Amperes. 

FIG.  117.— Curves  connecting  Total  Light  emitted  by  the  Arc  with  the 
Current  for  a  Constant  P.D.  of  45  Volts  between  the  Carbons. 
Carbons  :  Positive,  cored  ;  negative,  solid. 


368  THE  ELECTEIC  AEG. 

There  is,  probably,  however,  absorption,  and  this  absorption 
must  also  increase  with  the  current,  for  the  cross  section 
of  the  arc  certainly  increases  with  the  current.  Whether  the 
extra  amount  of  light  absorbed  ever  balances  the  extra  amount 
emitted  through  an  increase  of  current,  so  that  the  total 
light  received  outside  the  arc  rises  to  a  maximum  with  some 
particular  current  and  then  diminishes  can  only  be  determined 
by  experiment.  To  answer  this  question,  therefore,  we  must 
turn  to  the  actual  measurements  of  the  light  with  constant 
lengths  of  arc  and  different  currents. 

The  curves  that  Prof.  Ayrton  found  connecting  the  mean 
spherical  candle-power  of  the  arc  with  the  current  for  constant 
lengths  of  arc  of  1mm.  and  4mm.,  are  given  in  Fig.  116.  They 
are  plotted  from  Table  L.  (p.  328),  so  that  the  carbons  employed 
were  13mm.  cored  and  llmm.  solid.  These  curves  show  by 
their  form  that  with  small  currents  the  light  increases  more 
rapidly  than  the  current,  while  with  large  currents  the  reverse 
is  the  case,  but  there  appears  to  be  no  maximum  of  light  with 
any  particular  current.  Thus  we  are  led  to  the  conclusion 
that  with  a  given  length  of  arc  the  light  continues  to  increase 
as  the  current  increases,  till  hissing  occurs  and  changes  all 
the  conditions. 

M.  Blondel*  found  exactly  the  same  result  with  a  constant 
P.D.  and  varying  current,  as  may  be  seen  from  Fig.  117, 
which  gives  some  of  his  curves.  The  light  increases  much 
more  rapidly  with  the  current  in  these  curves  than  in  Prof. 
Ayrton's,  because  M.  Blondel  had  to  increase  the  length 
of  his  arc  with  the  larger  currents  in  order  to  keep  the  P.D. 
constant.  The  net  result  is  the  same,  however  :  there  is  no 
maximum  of  light  with  any  particular  current — the  light 
continues  to  increase  as  long  as  the  current  does  so. 

THE  LIGHT  EFFICIENCY  OF  THE  ARC. 

So  far,  our  whole  attention  has  been  devoted  to  the  quantity 
of  light  emitted  by  the  arc,  without  any  consideration  for  the 
amount  of  energy  expended  in  producing  that  light — the 
efficiency  of  the  arrangement.  We  shall  now  proceed  to 
examine  the  conditions  under  which  the  greatest  efficiency 

*  L'fidairage  Electrize,  1897,  Vol.  X.,  p.  297. 


LIGHT-EFFICIENCY  OF  THE  ARC.  369 

can  be  obtained.  This  has  already  been  done  in  Chapter  IX. 
(p.  264)  as  far  as  the  ratio  of  the  power  developed  in  the 
dynamo  to  the  power  expended  in  the  arc  is  concerned ;  but 
it  still  remains  to  be  seen  what  arrangements  enable  the  arc  to 
turn  a  given  amount  of  energy  supplied  to  it  into  the  greatest 
quantity  of  light. 

It  is  surprising  to  find  how  small  a  part  of  the  energy 
absorbed  by  even  such  an  efficient  source  of  light  as  the  arc  is 
utilised  in  producing  light.  Some  tests  made  by  Mr.  Hatsune 
Nakano  *  of  the  ratio  of  light-giving  radiation  to  the  total 
radiation  in  the  arc,  with  various  kinds  and  sizes  of  carbons, 
showed  that  this  ratio  varied  between  O'OIS  and  0*198,  or, 
roughly,  he  found  that  the  light-giving  radiation  was  from 
2  per  cent,  to  20  per  cent,  of  the  whole.  The  45  tests 
he  made  gave  an  average  of  10  per  cent,  for  the  light-giving 
radiation. 

Now,  the  most  economical  way  of  feeding  an  arc  is,  of  course, 
to  use  a  dynamo  driven  by  a  steam  engine.  Leaving  out 
of  account  all  losses  in  the  dynamo  and  mains,  the  engine  can 
only  transmit  to  the  dynamo  about  10  per  cent,  of  the  energy 
of  the  coal ;  and  it  follows  that,  since  only  10  per  cent,  of  this 
is  utilised  in  the  arc  to  produce  light,  an  average  of  only  one 
per  cent,  of  the  energy  of  the  coal  is  transformed  into  light 
energy,  and  the  other  99  per  cent,  is  wasted.  Truly  there  is 
a  wide  field  for  improvement  in  our  ways  of  producing  light ! 

Mr.  Nakano's  experiments  consisted  of  four  distinct  opera- 
tions. First,  he  measured  the  total  radiant  energy  of  the  arc 
by  means  of  a  thermopile  attached  to  a  sensitive  galvan- 
ometer. Next,  he  placed  an  alum  bath  between  the  arc  and 
the  thermopile,  to  screen  off  the  "  dark  heat,"  and  measured 
the  remaining  energy.  As,  however,  the  alum  bath  allowed 
a  certain  quantity  of  "dark  heat"  to  pass,  and  screened  off  a 
certain  portion  of  the  light,  a  correction  for  each  of  these  was 
needed.  The  first  was  made  by  placing  a  cell  containing  an 
opaque  solution  of  metallic  iodine  in  bi-sulphide  of  carbon 
between  the  lamp  and  the  alum  bath.  This  stopped  all  the 
light  rays,  but  allowed  all,  or  a  very  large  proportion,  of  the 
dark  heat  rays  to  pass.  Any  deflection  of  the  thermopile 

*  Paper  read  before  the  American  Institute  of  Electrical  Engineers, 
New  York,  May  22iul  1889. 


370  THE  ELECTRIC  AllC. 

must  now  be  caused  by  the  dark  heat  rays  that  passed 
through  the  alum  bath.  These  were  so  few  that  they  were 
found  to  be  imperceptible  in  most  cases.  Fourthly,  the 
quantity  of  light  that  was  absorbed  by  the  alum  bath  was 
measured  photometrically,  and  was  found  to  be  about  26  per 
cent.,  on  an  average. 

Until  Mr.  Nakano's  experiments  were  made,  we  had  no  idea 
how  much  of  the  energy  given  to  the  arc  was  utilised  in 
producing  light :  it  might  have  been  10  per  cent.,  it  might 
have  been  90  per  cent.  His  measurements  are,  therefore,  of 
immense  scientific  value,  and  of  great  value  also  in  showing  the 
direction  that  improvements  in  our  method  of  producing  light 
should  take.  For  practical  purposes,  however,  something  more 
is  required ;  light  energy  needs  to  be  translated  into  candle 
power.  The  light  consumer  wants  to  know,  not  how  much 
of  the  power  he  supplies  to  the  arc  will  be  utilised  in  pro- 
ducing light,  but  how  much  actual  light  he  will  get  for 
a  given  power  supplied.  By  making  measurements,  con- 
necting candle  power  with  luminous  energy,  it  might  be 

possible  to  translate  the  ratio  Iuminous  ener^  into  the  ratio 

total  energy 

light  emittted    1,1  ,  •     , . 

— — — -,  but   there   are   many   objections    to    such   a 
power  supplied 

method  of  finding  the  latter  ratio,  not  the  least  being  its 
circuitousness.  No,  this  ratio  is  best  found  by  measuring 
directly  either  the  total  light  emitted  and  the  power  absorbed 
by  the  arc,  as  M.  Blondel  does,  or  the  mean  spherical  candle 
power  and  the  power  absorbed,  as  most  other  experimenters 
do ;  and  for  either  of  these  measurements  the  eye  and  not  the 
thermopile  must  be  the  instrument. 
Distribution  of  the  Power  Supplied  to  the  Arc  between  the  Carbon 

Ends  and  the  Mist. 

Before  turning  to  these  experiments  it  will  be  interesting  to 
see  how  the  power  absorbed  in  the  arc,  under  given  conditions, 
is  distributed  among  the  five  sources  of  light  enumerated  on 
p.  314,  and  how  that  distribution  changes  with  a  change  in  the 
conditions.  The  power  absorbed  by  the  hot  ends  of  the 
carbons,  including,  of  course,  the  crater  and  the  white  spot, 
may  be  measured  by  multiplying  by  the  current  the  P.Ds. 
between  those  carbons  and  the  arc  mist.  The  power  given 


DISTRIBUTION  OF  POWER  IN  THE  ARC.  371 

to  the  arc  mist  may  be  obtained  by  subtracting  the  power 
absorbed  by  the  two  hot  ends  of  the  carbons  (including 
crater  and  white  spot)  from  the  total  power  supplied  to 
the  arc.  Now  it  seems  most  likely  that  the  end  of  the 
positive  carbon,  exclusive  of  the  crater,  is  only  imperceptibly 
heated  by  the  passage  of  the  current,  and  that  it  is  kept  hot 
by  heat  supplied  to  it  by  the  crater.  Similarly,  the  end  of 
the  negative  carbon  is  kept  hot  by  the  white  spot.  We  may, 
therefore,  consider  that  all  the  electric  energy  directly  supplied 
to  the  hot  ends  is  consumed  in  the  crater  and  the  white  spot, 
and  is  therefore  usefully  employed  in  giving  light,  while  that 
supplied  to  the  arc  mist  may  be  considered  as  practically 
wasted,  since  so  small  a  part  of  the  total  light  is  emitted  by 
the  mist. 

In  Chapter  VII.,  p.  231,  it  was  shown  that,  of  the 

(sS^-On*11'66*10'54*)  volts 

always  needed  to  maintain  an  arc  of  £mm.,  with  a  current  of 
A  amperes,  with  solid  carbons  11/9, 

1-66     3-n\ 

"A— +  -A-        VOltS, 


at  most,  were  expended  at  the  junctions  of  the  carbons  with 
the  arc  mist,  and 

volts, 


at  least,  were  used  in  sending  the  current  through  the  mist. 
Multiplying  each  of  these  expressions  by  A  we  get 

(38-88A  + 11-66 +  3-10  watts 
as  the  power  supplied  to  the  carbon  ends,  and 

(2-07  AZ  + 7-440  watts 

as  the  power  used  up  in  the  mist.  Thus,  every  increase  of  1mm. 
in  the  length  of  the  arc  is  accompaniedjby  an  increase  of  31  watts, 
at  most,  in  the  power  supplied  to  the  carbon  ends,  and  of 
(2-07A  +  7'44)  watts  in  the  power  used  in  the  mist.  But  the 
mist  in  itself  gives  out  so  little  light  that  this  latter  amount 
of  power  may  be  considered  wasted.  Thus,  almost  the  whole 
of  the  increased  power  that  has  to  be  supplied  to  the  arc  ivhen  it 
is  lengthened  is  swallowed  up  by  the  mist  and  is  practically  wasted 

BB2 


372  THE  ELEGTEIG  AEG. 

Moreover,  since  the  increased  power  used  in  the  carbon  ends 
does  not  depend  on  the  current,  and  that  used  in  the  mist 
does,  it  follows  that  the  waste  is  greater  the  greater  the 
current.  For  instance,  with  a  current  of  5  amperes  each 
increase  of  1mm.  in  the  length  of  the  arc  entails  an  increased 
waste  of  IT'S  watts  in  the  mist  and  an  increased  use  of 
3-1  watts  at  the  carbon  ends.  With  a  current  of  20  amperes 
the  power  used  in  the  carbon  ends  is  still  3'1  watts  per  mm., 
but  the  waste  in  the  mist  is  48'8  watts  per  mm. 

When  1  =  0,  (2-07A  +  7'44)  1  =  0  also,  that  is,  the  number 
expressing  the  power  supplied  to  the  mist  is  zero,  when  the 
length  of  the  arc  is  0,  even  although  length  of  arc  0  does  not 
mean  that  the  carbons  are  touching,  but  only  that  the  tip  of 
the  negative  carbon  and  the  mouth  of  the  crater  are  in  the 
same  plane.  This  can  only  mean  that,  the  power  supplied  to 
the  mist  that  lies  in  the  hollow  of  the  crater  is  always  so 
small  as  to  be  inappreciable. 

The  least  fraction  of  the  whole  power  that  is  always  practi- 
cally wasted  in  the  mist  is 


38-88A  +  11-66  +  (2-07A  +  10-54) 

With  a  3mm.  10-ampere  arc  (a  very  ordinary  one  for  the  size 
of  the  carbons)  this  fraction  is  0'17,  showing  that,  with  such 
an  arc  about  one-sixth  of  the  whole  power  consumed  is 
practically  wasted  in  the  mist,  quite  apart  from  the  fact  that 
not  all  the  light  created  can  get  out  and  be  made  use  of. 
Figs.  118  and  119  bring  out  with  great  clearness  the  way  in 
which  power  is  wasted  by  lengthening  the  arc,  as  far  as  the 
amount  of  light  created  is  concerned. 

The  upper  line  in  Fig.  119  shows  the  connection  between 
the  whole  power  given  to  the  arc  and  the  length  of  the  arc, 
with  a  constant  current  of  10  amperes.  The  lower  curve 
shows  the  power  wasted  in  the  mist  in  each  length  of  arc. 
The  distance  between  the  corresponding  points  on  each  line 
shows  the  part  of  the  power  that  is  used  at  the  carbon  ends, 
and  that  is  therefore  usefully  employed.  The  very  small 
difference  in  the  distance  between  the  corresponding  points  on 
the  two  lines  for  Omm,  and  10mm.  shows  how  very  little  the 
quantity  of  light  created  in  the  arc  is  increased  by  lengthening 
it  from  Omm.  to  10mm. 


POWER  WASTED  IN  ARC  MIST. 


373 


Fig.  119   shows   the   fraction  of  the  whole  power  that  is 
wasted  as  the  arc  is  lengthened  from  Omm.  to  10mm.  under 


800 


700 


GOO 


50° 


.g    400 


300 


200 


100 


9 


10 


01234567 

Length  of  Arc  in  Millimetres. 

FIG.  118.  —  Upper  Line  connects  Power  supplied  to  Arc  with  Length  of  Arc  ; 

Lower  Line  connects  Power  wasted  in  Mist  with  Length  of  Arc. 

Constant  Current,  10  amperes. 


012  345 

Lenqth  of  Arc  in  Millimetres. 

FIG.  119.— Curve  showing    the  Proportions   of    the  whole  Power  that 

is  wasted  in  the  Mist  with  each  Length  of  Arc. 

Constant  Current,  10  amperes. 


374  THE  ELECTRIC  AEG. 

the  same  conditions  as  governed  Fig.  118.  The  distance  0  A 
is  taken  to  represent  the  ivhole  power  supplied  to  the  arc, 
whatever  that  power  may  be,  and  the  part  of  this  distance 
that  is  shaded  represents  the  fraction  of  the  power  that  is 
wasted  in  the  mist  in  the  arc  of  corresponding  length.  The 
way  in  which  the  shaded  portion  grows  in  width  gives  a  very 
good  idea  of  the  manner  in  which  the  power  is  wasted,  as  far 
as  the  creation  of  light  is  concerned,  by  lengthening  the  arc. 

Condition  necessary  for  the  Arc  between  Given  Carbons  to  emit 
the  Maximum  of  Light  for  a  given  Power  developed  by  the 
Generator. 

Not  only  is  the  ratio  of  the  light  created  to  the  power 
consumed  in  the  arc  greatest  in  the  shortest  arc,  but  it  has 
been  shown  in  Chap.  IX.  (p.  260)  that  the  ratio  of  the  power 
consumed  in  the  arc  to  the  power  generated  in  the  dynamo  is 
also  a  maximum  with  the  shortest  arc ;  and,  further,  the 
quantity  of  crater  light  that  is  absorbed  by  the  arc  mist  is 
also  least  in  the  shortest  arc.  Everything,  therefore,  tends  to 
make  the  arc  the  more  efficient  the  shorter  it  is.  This  leads 
us  to  the  conclusion  that,  but  for  the  negative  carbon  stopping 
some  of  the  light,  the  ideal  condition  for  an  arc  ivould  be  to  have 
the  carbons  nearly  touching. 

Influence  of  Cross  Sections  of  Carbons  on  Lighting  Power  of  Arc. 

The  next  question  to  be  considered  is  the  influence  of  the  sizes 
of  the  carbons  on  the  lighting  power  of  the  arc.  Schreihage* 
attacked  this  problem  in  1888,  in  the  following  way.  He  took 
five  pairs  of  cored  positive  and  solid  negative  carbons,  the 
positives  varying  in  diameter  from  7*  12 mm.  to  18mm.  and  the 
negatives  from  5 '7 5mm.  to  16*1  mm.  The  ratio  of  the  cross 
section  of  the  positive  carbon  to  that  of  the  negative  was  as 
constant  as  possible,  varying  between  the  limits  1*54  :  1  and 
1-24  :  1,  as  is  shown  by  the  diagrams  of  them  published  in  the 
account  of  the  experiments.  Using  the  same  current,  6-29 
amperes,  and  the  same  mean  P.D.  between  the  carbons,  43-9 
volts  with  each  pair,  Schreihage  gathered  that  the  mean  hemi- 
spherical candle  power  varied  inversely  as  the  diameter  of  the 

*  Centrcdblatt  filr  Elektroteclmik,  1888,  Vol.  X.,  p.  591, 


EFFECT  OF  SIZES  OF  CARBONS  ON  LIGHT.        375 

positive  carbon  within  about  9  per  cent,  on  either  side  of  the 
mean. 

This  is  a  very  simple  and  beautiful  relation,  but  it  obviously 
cannot  be  applied  universally  without  further  investigation,  if 
only  because  there  is  nothing  in  the  experiments  to  show 
whether  it  is  the  size  of  the  positive  carbon  or  of  the  negative, 
or  of  both,  that  determines  the  lighting  power  of  the  arc. 
The  ratio  of  the  diameters  of  the  two  carbons  varied  only 
between  the  limits  1-12:1  and  1-24  : 1,  so  that  the  quantity 
L  d,  i.e.,  mean  spherical  candlepower  multiplied  by  diameters 
of  carbon  would  be  equally  constant  whether  the  d  was 
interpreted  to  mean  the  diameter  of  the  positive  carbon  or  of 
the  negative  carbon,  or  the  mean  of  the  two — as  long  as  the 
same  interpretation  was  taken  for  the  whole  five  pairs  of 
carbons.  What  Schreihage  really  showed,  and  it  was  a  great 
advance  at  the  time,  was  that  there  was  some  sort  of  inverse 
proportionality  between  the  lighting  power  of  the  arc  and  the 
diameters  of  the  carbons,  when  the  current  and  P.D.  were 
constant.  He  also  called  attention  to  the  increasing  bluntness 
of  the  positive  carbon,  and  to  the  way  in  which  the  length  of 
the  red-hot  part  of  that  carbon  diminished  as  its  diameter 
increased. 

The  effect  on  the  lighting  power  of  the  arc  of  varying  the 
diameter  of  each  of  the  carbons  separately  was  first  tried  by 
M.  Blondel*  in  1897,  as  part  of  the  exhaustive  series  of  experi- 
ments to  which  I  have  made  such  frequent  reference.  M.  Blondel 
found  that  the  light  could  be  increased  with  the  same  current 
and  P.D.  between  the  carbons,  either  by  reducing  the  size 
of  the  negative  carbon  with  a  constant  positive,  or  by  reducing 
the  size  of  a  cored  positive  carbon  with  a  constant  negative.  He 
found,  for  instance,  that  with  a  current  of  10  amperes,  a  P.D. 
of  40  volts  and  a  positive  carbon  of  16mm.,  the  light 
could  be  increased  from  5,019  lumens  with  a  negative  carbon 
of  16mm.  to  6,575  lumens  with  one  of  6mm. ;  and  with 
the  same  P.D.  and  current,  and  a  negative  carbon  of  6mm.  the 
light  could  be  increased  from  6,575  lumens  with  a  positive 
carbon  of  16mm.  to  10,462  with  one  of  6mm,  The  relative 
importance  of  the  sizes  of  the  two  carbons  in  regulating  the 

*  .L'tfdairage  Electriyuc,  1897,  Vol.X.,  p.  497. 


376 


THE  ELECTRIC  ARC. 


total  quantity  of  light  emitted,  cannot,  of  course,  be  determined 
from  the  above  numbers,  because  the  size  of  the  constant  carbon 
was  not  the  same  in  both  cases,  but  they  appear  to  show  that 
the  diameters  of  the  two  carbons  are  at  least  equally  important 
in  determining  the  lighting  power  of  the  arc.  This  appearance 
is,  however,  to  a  certain  extent  fallacious,  and  indeed,  while 
we  know  perfectly  well  that  increasing  the  diameter  of  the 
negative  carbon  must  diminish  the  light  of  the  arc  by 
obstructing  that  of  the  crater,  it  is  difficult  to  see  how 
increasing  the  diameter  of  the  positive  carbon  can  have  an 
effect  anything  like  as  great.  It  is  true  that  quite  apart  from 


FIG.  120. — Diagrams  of  Arc  with  the  same  Current  (10  amperes)   and 

Length  (2mm.),  but  with  Different  sized  Carbons. 

Positive  Carbon  cored  ;  negative  solid. 

the  shortening  of  the  red  hot  part  of  the  positive  carbon 
mentioned  by  Schreihage,  there  are  two  other  ways  in  which 
the  light  of  the  arc  must  be  diminished  by  increasing  the 
diameter  of  the  positive  carbon.  The  light  of  the  white  spot 
must  be  more  screened,  and  the  mist  being  obstructed  in  its 
upward  flow  must  be  wider  and  so  absorb  more  light.  But  it 
is  quite  inconceivable  that  all  these  three  causes  together 
should  be  sufficient  to  account  for  the  immense  difference  in 
the  light  observed  by  M.  Blondel.  That  the  mist  has  actually 
a  larger  cross  section,  and  the  obvious  reason  of  it,  will  be  seen 


EFFECT  OF  SIZE  OF  CORE  ON  THE  LIGHT.        377 

from  Fig.  1 20,  the  diagrams  in  which  are  diminished  copies  of 
images  of  the  arc  and  carbons  taken  with  a  current  of 
10  amperes,  a  P.D.  of  43  volts  and  an  arc  of  2mm.  For 
the  diagram  on  the  left  the  carbons  were  18mm.  cored  and 
15mm.  solid,  and  for  that  on  the  right  they  were  13mm.  cored 
and  llmm.  solid.  It  is  evident  that  the  wider  positive  carbon 
has  caused  the  arc  mist  to  have  a  much  larger  cross  section, 
and  that  therefore  the  crater  light  must  lose  more  by  absorp- 
tion when  this  larger  carbon  is  used. 

This,  however,  is  not  the  most  important  reason  for  the 
great  change  in  the  light  flux  noticed  by  M.  Blondel  when  he 
increased  the  size  of  the  positive  carbon.  The  reason  seems, 
rather,  to  be  that  while  the  negative  carbons  used  for  the 
experiments  were  solid,  the  positive  carbons  were  cored,  and 
as  they  were  ordinary  commercial  carbons — "  Nanterre  "  was 
the  brand — and  not  made  specially  for  experimental  purposes, 
the  core  was  certainly  made  to  have  some  sort  of  proportion- 
ality to  the  diameter  of  the  carbon  :  it  would  be  larger  in  the 
larger  carbon  than  in  the  smaller  one.  Now,  it  will  be 
presently  shown  (p.  386)  that  the  surface  of  the  core  gives 
a  much  less  brilliant  light  than  the  remainder  of  the  surface 
of  the  crater,  and  M.  Blondel  himself  has  shown  that  the  arc 
gives  less  light  the  thicker  the  core.  Thus,  of  two  craters  of 
nearly  the  same  size,  the  one  with  the  larger  core  would  give 
the  less  light;  so  that  the  18mm.  carbon  with  a  core  probably 
4mm.  in  diameter  would  naturally  give  less  light,  all  other 
conditions  being  equal,  than  the  6mm.  carbon  with  a  core  of, 
say,  l-5mm.  It  was  not,  therefore,  the  increase  in  the  size 
of  the  positive  carbon  that  was  the  principal  cause  of  the 
diminution  in  the  amount  of  light  emitted  by  the  arc  in 
M.  Blondel's  experiments,  but  the  larger  core  that  that 
increase  entailed.  Clearly,  to  see  the  effect  produced  by  size 
alone,  it  would  be  necessary  to  repeat  the  experiments,  using 
a  solid  instead  of  a  cored  positive  carbon. 

The  whole  question  is,  however,  fraught  with  difficulties 
and  complications,  and  should,  I  think,  be  attacked  in  a  some- 
what different  manner.  For  instance,  we  have  seen  how  much 
more  directly  the  light  depends  on  the  length  of  the  arc  than 
on  the  P.D.  between  the  carbons.  We  have  also  seen  (p.  161) 
that  the  P.D.  between  the  carbons  is  influenced  by  the 


378  THE  ELECTRIC  ARC. 

diameters  of  the  carbons  with  some  currents,  and  not  with 
others,  and  that  it  always  depends  to  some  extent  on  the  size 
of  the  core.  It  seems  highly  probable,  therefore,  that  by 
choosing  the  current  and  the  carbons  properly  we  could  almost 
make  the  light  vary  in  any  way  we  chose,  while  getting  an 
effect  apparently  due  to  a  change  in  the  size  of  the  positive 
carbon  alone.  In  order,  then,  to  see  how  a  simple  increase  in 
the  size  of  the  positive  carbon  alone  affects  the  lighting  power 
of  the  arc,  the  following  precautions  must  be  taken  : — 

(1)  Both  carbons  must  be  solid  and  of  the  same  make  and 
hardness  for  all  the  experiments. 

(2)  The  current  and  length  of  arc  must  be  chosen  in  such  a 
way  that  the  length  of  arc,  as  well  as  the  current  and  the  P.D. 
between  the  carbons,  can  be  constant  for  all  the  experiments. 

(3)  The  negative  carbon  must  have  a  constant  diameter,  as 
it  had  in  M  Blondel's  experiments. 

With  these  precautions  which,  though  difficult  it  would  not 
be  impossible  to  take,  we  should  really  be  able  to  judge  of  the 
extent  to  which  a  given  increase  in  the  size  of  the  positive 
carbon  diminished  the  lighting  power  of  the  arc.  That  it  must 
diminish  it  to  a  certain  extent  has  been  shown  from  a  priori 
considerations,  and  hence,  without  making  such  very  accurate 
experiments,  it  is  quite  safe  to  take  it  for  granted  that  in 
order  to  insure  the  greatest  light  efficiency  in  the  arc  the 
positive  carbon  must  be  as  small  as  it  conveniently  can.  Now 
there  is  a  limit  to  the  thinness  of  the  positive  carbon  that 
does  not  exist  in  the  case  of  the  negative.  I  allude  to  the 
possibility  of  hissing,  which  has  been  shown  (p.  299)  to  depend  on 
the  size  of  the  positive  carbon  with  a  fixed  current  and  length 
of  arc.  The  larger  the  current  the  greater  must  be  the 
positive  carbon  in  order  that  the  arc  may  remain  silent.  It 
comes  to  this,  then  ;  with  a  fixed  current,  length  of  arc  and 
P.D.  between  the  carious,  and  a  given  negative  carbon,  the  arc 
will  give  most  light  ivhcn  the  positive  carbon  is  as  small  as  it  can 
be  without  causing  the  arc  to  be  so  near  the  hissing  point  as  to  be 
unsteady. 

The  diagrams  in  Fig.  121  show  the  sort  of  change  that  takes 
place  in  the  shapes  of  the  carbons  when  the  sizes  of  these  are 
altered,  and  when  the  current  and  the  length  of  the  arc  are  kept 
constant.  The  current  employed  was  6  amperes,  and  the 


LIGHT  GREATER  THE  SMALLER  THE  NEGATIVE.  379 

length  of  the  arc  1mm.  The  carbons  were  18/15,  13/11,  and 
9/8,  the  positive  being  cored  and  the  negative  solid  in  each 
case.  Enlarging  the  carbons  seems  to  slightly  enlarge  the 
crater,  which  would  cause  an  increase  in  the  amount  of  light 
emitted,  were  it  not  that  the  significant  angles  BAD  and 
EBD  both  diminish  when  the  carbons  are  enlarged.  Also 
when  the  light  is  received  in  any  given  direction  between  A  D 
and  B  D,  it  is  easy  to  see  that  a  large  negative  carbon  would 
hide  far  more  of  the  crater  than  a  small  one. 

Thus  this  figure  shows,  as  M.  Blondel's  experiments  did,  that 
with  a  fixed  current,  length  of  arc,  and  P.D.,  between  the  carbons, 
the  arc  gives  more  light  the  smaller  the  negative  carbon. 


FIG.  121.— Diagrams  of  Arcs  with  the  same  Current  (6  amperes)  and 
Length  (1mm.),  but  with  Different  sized  Carbons. 
Positive  Carbon  cored  ;  negative  solid. 

In   Chap.   IX.  (p.  260)  it  was  shown  that  the   supply  of 
power   to   the   arc   was  most   efficiently   conducted,  i.e.,  the 

power  supplied  to  arc  ,        L, 

ratio   " h!r was   greatest,  when  the 

power   developed    by  dynamos 

current  was  the  largest  that  would  certainly  give  a  silent  arc. 
This  is  only  another  way  of  saying  that  with  a  given  current 
the  arrangement  for  the  supply  of  power  was  most  efficient 
when  the  positive  carbon  was  the  smallest  with  which  there 
would  be  no  danger  of  hissing  with  the  given  current,  The 


380  THE  ELECTRIC  AEC. 

law  of  the  smallest  carbons,  therefore,  applies  not  only  to  the 
light  efficiency,  but  also  to  the  power  efficiency  of  the  arc.  In 

J.L  11.1    ,1         L>  power  used  in  arc  -, 

other  words  both  the  ratio  -  — and 

power  developed  by  dynamo 

the  ratio  'ight  generated  in  arc  ^  ^  when  ^  ^^ 

power  supplied  to  arc 

are  the  smallest.   Hence  the  ratio       "ght  generated  in  are 

power  developed  m  dynamo 

is  also  greatest  under  the  same  conditions.  In  every  way 
possible,  therefore,  the  arc  burns  most  economically  when  the 
carbons  are  the  very  smallest  that  can  carry  the  current,  with- 
out danger  of  hissing,  in  the  case  of  the  positive,  and  without 
burning  too  fast,  in  the  case  of  the  negative. 

The  prime  necessity  in  order  to  ensure  a  highly  efficient  arc 
is,  therefore,  to  have  both  carbons,  especially  the  negative,  as 
thin  as  the  current  will  allow,  and  then,  as  the  negative  carbon 
cannot  be  infinitely  thin,  it  must  be  a  matter  for  experiment  to 
see  with  what  length  of  arc  the  disadvantage  of  the  extra  power 
wasted  in  that  length  is  exactly  counterbalanced  by  the 
advantage  due  to  the  extra  amount  of  light  let  out ;  for  this 
will  be  the  length  that  will  give  the  maximum  efficiency  under 
the  given  conditions.  One  would  naturally  suppose  that  this 
length  of  arc  would  be  shorter  the  smaller  the  carbons,  and  that 
it  is  so,  at  least  when  both  carbons  are  solid,  is  proved  by  the 
curves  in  Fig.  122,  which  are  taken  fromM.  Blondel's  *  results. 

These  curves  give  the  connection  between  the  light  efficiency 

(total  light  emittedN      r     ,  ,    .,      ,       ,1         .^ 
2 )    of    the   arc,   and   its   length,    with    a 
power  consumed   / 

constant  current  of  10  amperes,  for  three  different  sets  of  solid 
"Nanterre"  carbons,  8/6,"  10/10,  and  16/14.  They  show  at 
a  glance  what  M.  Blondel  deduced  from  the  same  results 
plotted  with  the  P.D.  between  the  carbons,  instead  of  with 
the  length  of  the  arc,  viz.,  that  whatever  the  length  of  the 
arc  (except  zero  in  one  case)  the  light  efficiency  is  always 
greatest  with  the  smallest  carbons,  and  that  the  maximum 
efficiency  for  a  given  pair  of  carbons  is  also  much  the  greatest 
with  the  smallest  carbons,  ranging  as  it  does  from  about  2 6 '6 
lumens  per  watt  with  the  8/6  carbons  to  only  about  14 '6  lumens 
per  watt  with  the  16/14  carbons.  In  other  words,  the  maximum 
*  L'ficlairage  filectrique,  1897,  Vol.  X.?  p.  290. 


LIGHT  EFFICIENCY  AND  LENGTH  OF  ARC.       381 

efficiency  in  this  case  is  nearly  doubled  by  halving  the  diameter 
of  the  positive  carbon  and  by  taking  that  of  the  negative  carbon 
rather  less  than  half.  Lastly,  these  curves  show  that  with  solid 
carbons  the  maximum  efficiency  of  the  arc  is  reached  with  a 
shorter  arc  the  smaller  the  carbons.  For  with  the  8/6  carbons 
this  maximum  is  attained  with  a  1mm.  arc,  with  the  10/10 
with  a  3-5  mm.  arc,  and  with  the  16/14  carbons  the  arc  has 
to  be  5-5mm.  in  length  before  the  maximum  efficiency  is 
gained.  Thus  practical  experience  fully  corroborates  the 
conclusions  drawn  from  theoretical  considerations  as  to  the 
need  of  using  small  carbons  and  short  arcs  in  order  to  obtain 
the  maximum  light  efficiency  with  solid  carbons. 

SOLID  CARBONS.     (Blondel.) 


012345 

Length  of  Arc  in  Millimetres. 

Fia.  122. — Curves  connecting  Light  Efficiency  with  Length  of  Arc. 
Current,  10  amperes. 

When  the  positive  carbon  is  cored  the  conclusions  are  not 
all  quite  so  definite,  as  will  be  seen  from  Fig.  123,  the  curves 
in  which,  like  those  in  Fig.  122,  are  drawn  from  M.  Blondel's* 
researches.  The  current  employed  was  again  10  amperes,  and 
the  carbons  were  8/6,  10/10,  14/12,  and  18/14.  It  may  be 
gathered  from  these  curves  that  the  efficiency  for  any  par- 
ticular length  of  arc  is  always  greater,  and  the  maximum 
efficiency  is  higher,  the  smaller  the  carbons,  when  the  positive 
*  L'tfclairage  Electrique,  1897,  Vol.  X.,  p.  296. 


382 


THE  ELECTRIC  ARC. 


carbon  is  cored  as  well  as  when  both  carbons  are  solid.  What 
is  not  quite  so  definite  with  the  cored  positive  carbon  is  the 
length  of  arc  with  which  the  maximum  efficiency  is  attained. 
This  seems  to  vary  between  0'5mm.  and  l'5mm.  with  all  the 
carbons  except  the  10/10,  which  have  very  much  the  same 
efficiency  for  any  length  of  arc  between  about  I'Tmm.  and  4mm. 
On  the  whole,  however,  Figs.  122  and  123  both  corroborate 
what  has  already  been  said  on  p,  380,  that  in  order  to  have  the 
greatest  possible  amount  of  light  for  the  power  supplied  to  the 
arc,  with  a  given  current,  the  positive  carbon  must  be  as  small 
as  it  can  be  without  fear  of  hissing ;  the  negative  carbon  must 

CORED  POSITIVE  CARBON.     (Blonde!.) 


01234567 
Length  of  Are  in  Millimetres. 

FIG.  123. — Curves  connecting  Light  Efficiency  with  Length  of  Arc. 
Current,  10  amperes. 

be  the  smallest  that  will  carry  the  current  without  burning 
away  too  fast ;  and  the  length  of  arc  must  be  that  which  is 
found  by  experiment  to  give  the  maximum  efficiency  with  the 
given  current  and  carbons.  With  solid  carbons  this  length  is 
less  the  smaller  the  carbons,  because  the  smaller  the  negative 
carbon  the  more  nearly  do  the  quantity  of  light  created  and 
the  quantity  that  escapes  from  between  the  carbons  approxi- 
mate to  one  another,  and  if  the  negative  carbon  could  be 
infinitely  small  all  the  light  created  would  escape,  and  then 
the  maximum  efficiency  would  be  obtained  with  length  of 
arc  0.  With  a  cored  positive  carbon  the  core  seems  to 


EFFICIENCY  OF  COMMERCIAL  ARC  LAMPS.        383 

interfere,  and  to  make  the  length  of  arc  with  which  the 
maximum  efficiency  is  obtained  depend  less  definitely  on  the 
sizes  of  the  carbons. 


Low  Efficiency  of  Commercial  Arc  Lamps  due  to  Thickness  of 
Carbons  employed. 

A  reference  to  Table  LIL,  the  data  for  which  were  collected 
by  Prof.  Ayrton  about  two  years  ago,  will  show  how  little 
the  need  of  thin  carbons  for  the  arc  to  burn  economically  was 
then  realised,  and  very  little  improvement  in  this  direction  has, 
I  believe,  taken  place  since.  This  table  gives  a  list  of  carbons 
of  different  makes  with  the  currents  intended  to  be  used  with 
them. 

Table  LII. — Sizes  and  Lengths  of  Carbons  employed  in  Com- 
mercial Arc  Lamps,  with  Currents  used,  Average  P.D. 
between  Carbons,  and  Time  of  Burning. 

Carbons:  Positive  cored ;  negative  solid. 


Diain.  of 
Pos.  Garb. 
in  mm. 

Diarn.  of     Length  of 
Neg.  Garb,  each  carbon 
in  mm.     '  in  inches. 

Current  in 
Amperes. 

P.D.  between 
Carbons  in 

Volts. 

Time  of 
Burning  in 
Hours. 

20 
18 
18 

13 
13 
12 

9-5 
9-0 
8-0 

10 
10 
10 

44 
43 

10-12 
10 

Now  suppose  that  these  arcs  were  all  burned  under  such 
conditions  that  the  maximum  efficiency  possible  with  such 
carbons  and  such  a  current  was  obtained.  This  maximum 
efficiency  would  probably  be  very  much  the  same  as  that  pro- 
duced with  the  18/14  carbons  used  by  M.  Blondel,  about 
14  lumens  per  watt,  or,  since  the  negative  carbon  in  the  lamps 
was  less  than  14mm.,  let  us  put  it  at  16  lumens  per  watt, 
which  is  a  liberal  allowance.  If  the  size  of  the  carbons  had  been 
8/6  instead  of  what  they  were,  the  current  and  P.D.  between  the 
carbons  being  unaltered,  the  quantity  of  light  emitted  per 
watt  would,  according  to  Fig.  123,  have  been  24  lumens,  or 
half  as  much  again,  so  that  by  using  smaller  carbons  the  same 
amount  of  light  could  be  obtained  with  the  expenditure  of 
two-thirds  of  the  power,  i.e.,  at  two-thirds  of  the  cost  for 


384  THE  ELECTRIC  ARC. 

power.  If  still  smaller  carbons  than  8/6  could  be  used,  the 
light  efficiency  would  be  still  greater,  and  probably  might  be 
doubled,  for  the  light  efficiency  increases  more  rapidly  than  the 
sizes  of  the  carbons  diminish.  The  reply  to  this  is,  of  course, 
that  smaller  carbons  cannot  be  manufactured  to  burn  any- 
thing like  10  hours  with  a  10-ampere  current  flowing.  This 
is  probably  true  at  the  present  time,  but  it  only  shows  the 
imperative  necessity  of  making  carbons  that  shall  be  both  thin 
and  slow  burning,  and  when  this  is  done  the  enclosed  arc  will 
no  longer  be  able  to  hold  its  own  against  the  open  arc ;  for 
there  can  be  no  possible  doubt  of  the  superior  efficiency  of 
the  open  arc  when  burnt  under  proper  conditions.  The  sole 
superiority  of  the  enclosed  arc  lies  in  the  labour  and  expense 
it  saves  by  the  slow  burning  of  its  carbons — a  great  superiority 
indeed,  and  one  which  counts  for  even  more  in  America  than 
in  England — but  one  that  should  yield  to  the  ingenuity  and 
patience  of  the  inventor. 

Variation  of  Light  Efficiency  with  Current. 

In  observing  the  way  in  which  the  efficiency  of  the  arc 
varies  under  different  conditions,  we  have  hitherto  dealt  with  a 
constant  current  of  10  amperes ;  it  is  necessary,  however,  to 
know  also  how  the  efficiency  varies  with  the  current.  Fig.  124, 
taken,  like  so  many  others,  from  M.  Blondel's  Papers,*  shows 
the  variation  in  the  efficiency  produced  by  changing  the 
current,  while  a  constant  P.D.  was  maintained  between  the 
carbons.  The  carbons  employed  were  ordinary  commercial 
cored  positive  and  solid  negative  carbons  for  the  first  three 
curves,  and  Siemens'  solid  carbons  for  IV.  The  sizes  were  6/6 
for  I.,  10/10  for  II.,  18/18  for  III.,  and  10/10  for  IV.  For  the 
first  three  curves  the  P.D.  was  kept  constant  at  45  volts,  and 
for  the  fourth  at  50  volts.  The  efficiency  of  the  arc  appears 
to  increase  very  rapidly  at  first,  as  the  current  is  increased, 
and  then  much  more  slowly,  while  it  even  has  a  maximum 
point,  and  then  diminishes  with  the  solid  Siemens'  carbons. 
This  maximum  point  is,  I  think,  explained  by  the  fact  that  as 
the  P.D.  was  kept  constant  and  the  current  increased,  the 
length  of  the  arc  had  to  be  increased  also,  for  with  a  con- 
stant length  of  arc  the  P.D.  always  diminishes  as  the  current 
*  L' Eclair  aye  Elcctriyuc,  Vol.  X.,  p.  498. 


LIGHT  EFFICIENCY  AND  CURRENT. 


385 


increases  with  solid  carbons.  Now  the  length  of  the  arc  rose 
from  2'8  to  3'3mm.  as  the  current  was  increased  from  12  to 
15  amperes;  and  we  have  seen  that  there  are  two  ways  in 
which  the  efficiency  is  diminished  by  lengthening  the  arc : 
Firstly,  more  of  the  power  is  wasted  in  the  mist,  and  secondly, 
the  longer  mist  column  absorbs  more  of  the  light  of  the  crater. 
At  the  same  time,  lengthening  the  arc  enables  more  of  the 
crater  light  to  escape.  It  is  thus  quite  probable  that  with 
(Blondel.) 


20 


Si 

1 

,2  10 


10 


2f> 


35 


15  20 

Current  in  Amperes. 

FIG.  124.— Curves  connecting  Light-Efficiency  with  Current  for  Constant  P.D. 

Carbons  ;  L,  6/6,  II.,  10/10,  III.,  18/18,  45  volts  ;  IV.,  10/10,  50  volts. 
I.,  II.,  III.,  Nanterre,  positive  cored,  negative  solid.     IV.,  Siemens,  both  solid. 

arcs  as  long  as  from  2*8  to  3*3mm.  the  diminution  of  efficiency 
due  to  the  first  two  causes  may  more  than  counterbalance  the 
increase  due  to  the  third  and  to  the  increase  of  the  current. 
It  is  not,  however,  easy  to  assign  phenomena  to  their  right 
causes  when  cored  carbons  are  used,  seeing  how  the  core  com- 
plicates everything  in  the  arc — the  P.D.  necessary  to  send  a 

cc 


386  THE  ELECTRIC  ARC. 

given  current  through  a  given  length  of  arc ;  the  amount  of 
absorption  due  to  the  two  sorts  of  mist  that  must  be  gener- 
ated, that  of  the  core  and  that  of  the  hard  outer  carbon  ;  the 
difference  of  intrinsic  brilliancy  between  the  two  parts  of  the 
crater  surface.  All  these  introduce  complications  that  it  is 
next  to  impossible  to  unravel,  and  hence  it  is  really  only  upon 
observations  made  with  solid  carbons  that  it  is  possible  to 
theorise,  except  in  so  far  as  one  can  show  ivhy  the  results 
obtained  with  cored  carbons  often  differ  so  widely  from  those 
gained  with  solid  ones. 

Efect  of  Composition  of  Carbons  on  the  Lighting  Power  of  the  Arc. 

The  lighting  power  of  tin  arc  depends  just  as  much  on  the 
composition  of  the  carbons  as  on  their  sizes,  or  on  the  current 
and  length  of  arc.  Carbons  may  be  hard  or  soft,  solid  or 
cored.  Dr.  Louis  Marks*  has  made  a  very  careful  study  of 
the  lighting  power  and  life  of  particular  sorts  of  carbons.  He 
finds  that  soft  carbons,  rich  in  lampblack,  give  a  better  light 
for  the  same  amount  of  power  than  harder  ones,  containing 
more  graphite.  M.  Blondel  attributes  this  to  the  quicker 
burning  away  of  the  softer  carbons,  their  pointing  themselves 
better,  and  having  a  more  distinct  crater.  The  American 
"Electra"  carbons,  he  finds,  give  a  great  deal  of  light  for  the 
power  they  consume,  but  burn  away  with  extraordinary 
rapidity.  M.  Blondel  finds  also  that  when  both  carbons  are 
solid  more  light  is  given  out,  for  the  same  power  applied,  than 
when  the  positive  is  cored,  and  that  the  diminution  of  the 
light  is  greater  the  larger  the  diameter  of  the  core.  This,  as  he 
pointed  out  in  1893,f  is  because  the  core  has  a  lower  degree  of 
incandescence,  which  must,  of  course,  mean  a  lower  temperature. 
Every  one  who  has  seen  an  image  of  the  crater  must  have 
observed  this.  If  the  current  is  large  enough  for  the  crater  to 
more  than  cover  the  core,  the  cored  part  looks  quite  dim 
compared  with  the  ring  of  solid  carbon  round  it. 

M.  Blondel  has  found  that  there  are  yet  other  ways  in 
which  the  make  of  the  carbons  influences  the  light-producing 
power  of  the  arc.  He  finds  that  it  is  very  important  that  they 
should  be  as  pure  as  possible,  pure  carbons  giving  a  far  better 

*  American  Institute  of  Electrical  Engineers,  July,  1890. 
t  Report  of  the  Electrical  Congress  at  Chicago,  1893. 


ARC  LAMPS  IN  SERIES.  387 

light  than  those  less  carefully  prepared.  He  also  lays  great 
stress  on  the  necessity  for  their  being  well-baked,  and  attributes 
the  superiority  of  the  Siemens  "  A  "  carbons  to  their  being  twice 
baked,  fche  double  baking  rendering  them  purer,  he  believes. 

Arc  Lamps  in  Series. 

One  great  difficulty  to  be  overcome  in  the  arrangement  of 

arc  lamps  to-day  is  the  high  P.D.  that  it  has  lately  become 

usual  to  maintain  between  the  mains — 200  and  sometimes  even 

230  volts.     This   necessitates   the   use   of  several   lamps   in 

series,  and  the  substitution  of  resistances  for  any  lamps  of  the 

series  that  do  not  happen  to  be  required.     The  waste  thus 

involved,    whenever   it  happens  that   all   the   lamps  are   not 

always  required  at  the  same  time,  is  enormous.     The  best  way 

to  overcome  the  difficulty,  would  probably  be  to  use  very  small 

currents  (and  consequently  very  small  carbons),  and  to  treat 

each  series  of  arcs  as  a  single  source  of  light.     Suppose,  for 

instance,  it  were  possible  to  have  a  good  steady  arc  with  a 

current  of,  say,  2'5  amperes  only,  the  carbons  being  so  small 

that  the  maximum  efficiency  of  the  arc  would  be  obtained  with 

quite  a  short  arc,  0'2mm.,  say.     Then  the  P.D.  between  each 

pair  of  carbons   would  probably  not  have  to  be  higher  than 

about  47  volts,  and  with   200-volt  mains  four  arcs  in  series 

could  be  employed,  using  188  volts,  and  leaving  12  volts  to  be 

used  up  in  the  mains  and  the  regulating  resistances.     The 

resistance  of  all  these  together    would  be   12-=- 2-5  ohms,  or 

4 '8  ohms.     The  power  supplied  to  the  groups  of  arcs  would 

be  500  watts,  and  of  that  30  watts  would  be  wasted  in  the 

resistances  &c.,  or  94  per  cent,  would  be  used  and  6  per  cent. 

would  be  wasted.     The  arcs  could  be  grouped  so  as  to  let  out 

the  largest  possible   amount  of  light,  and  they  would  use  the 

same    amount   of    power  as    a   single    50-volt  lamp   burning 

10  amperes.    It  seems  quite  clear  that,  if  a  not  too  complicated 

arc    lamp   could    be    devised    that    would  hold   and  regulate 

the  whole  four  arcs  at  once,  it  would  command  a  very  large 

sale    for  use  on  high  voltage  mains ;  for  the  convenience  of 

being  able  to  use  the  whole   large  P.D.   between  the  mains 

to   supply    each    single    group   of   lights    would    more  than 

counterbalance  any  small  waste   that  might  ensue  from  the 

arrangement  being  less  efficient  than  the  ordinary  large  current 

arcs  now  in  use. 

cc2 


388  THE  ELECTRIC  ARC. 

The  Only  Fair  Method  of  Comparing  the  Efficiency  of  tiro  Sources 

of  Light. 

One  word,  in  conclusion,  as  to  the  right  way  of  comparing 
two  sources  of  light.  As  yet  there  is  no  definite  standard 
method  which  is  adopted  by  the  scientific  and  the  practical 
man  alike.  Various  people  test  various  things  and  call  them 
candle  power.  Some  take  the  candle  power  in  the  direction  in 
which  it  is  greatest  and  call  that  the  candle  power  of  the 
source.  In  this  way  we  get  nominal  2,000  c.p.  arc  lamps, 
which  are  really  a  bare  600  c.p.  Others  take  the  mean 
spherical  candle  power  of  each  source,  it  is  true,  but  under 
conditions  which,  while  they  may  be  the  best  for  one  of  the 
sources,  may  be  the  worst  for  the  other.  This,  again,  is  unfair. 

There  is,  indeed,  only  one  fair  and  right  method  of  com- 
parison, and  that  is  to  arrange  the  conditions  of  each  source 
so  as  to  enable  it  to  do  its  best,  and  then  to  measure  the  mean 
spherical  candle  power,  or  total  quantity  of  light  (it  does  not 
matter  which),  emitted  by  each  ;  to  measure  at  the  same  time 
the  power  supplied  to  each,  and  to  divide  the  first  by  the 
second  to  obtain  the  light  efficiency  of  each  source.  This  is  the 
only  fair  way  of  comparing  their  relative  values.  For  what 
does  it  matter  to  a  user  of  light  that  one  lamp  will  give  him 
2,000  c.p.  and  another  only  500  ?  He  can  always  arrange  to 
have  four  of  the  latter  instead  of  one  of  the  former,  provided 
always  that  the  four  do  not  cost  him  more  than  the  one.  What 
he  wants  to  know  about  his  lamp  is  how  much  light  he  gets 
from  it  for  the  money  he  expends,  that  is,  for  the  power  it 
uses,  after  the  initial  cost  has  been  overcome.  Doubtless  there 
are  many  other  things  to  be  taken  into  account  in  choosing  a 
lamp  besides  its  efficiency — the  initial  cost,  cost  of  repairs,  cost 
of  up-keep  (labour  in  replacing  new  carbons,  &c.),  &c.  ;  but  in 
comparing  the  light  received  from  lamps,  the  only  true  test  of 
their  value  is  the  amount  of  light  per  watt  that  they  give  when 
each  is  in  the  conditions  best  suited  to  it. 


SUMMARY. 

I.  The  light  emitted  by  the  arc  in  any  given  direction  is 
roughly  proportional  to  the  apparent  area  of  the  crater  as  seen 
from  that  direction, 


SUMMARY.  389 

II.  On  the  whole,  the  light  emitted  by   the   arc,  with   a 
constant  current,  increases,  up  to  a  certain  point,  as  the  arc  is 
lengthened,  because  the  greater  distance  between  the  carbons 
allows  more  of  the  crater  light  to  escape. 

III.  As,  however,  the  negative  carbon  becomes  very  finely 
pointed  when  the  arc  is  short,  with  large  currents,  the  light 
emitted  by  a  very  short  arc  is  greater  than  that  of  a  longer  one, 
when  the  current  is  large. 

IV.  The  illuminating  power  of  the  arc    does  not  increase 
indefinitely  as  the  arc  is  lengthened,  with  a  contant  current, 
but  has  a  maximum  value  with  a  comparatively  short  length 
of  arc,  some  4mm.  or  so. 

V.  This  is  probably  due  to  the  absorption  of  the  light  of 
the  crater  by  the  carbon  mist,  which  it  traverses  before  escaping 
from  between  the  carbons. 

VI.  The  fact  that  the  arc  does  absorb  light  can  be  proved 
in  various  ways.     (1)  It  casts  a  shadow;   (2)  it  hides  things 
placed  behind  it ;    (3)  the  light  becomes  more  purple  as  the 
arc  is  lengthened,  as  if  more  of  the  yellow  and  green  rays  of 
the  crater  light  were  absorbed,  the  longer  the  arc. 

VII.  When    either    the    length   of    the   arc   or    the    P.D. 
between    the    carbons    is    constant,   the   illuminating    power 
increases  with  the  current. 

VIII.  Only  about  10  per  cent,  of  the  energy  supplied  to 
the  arc  is  utilised  in  producing  light. 

IX.  Of  the  power  supplied  to   the  arc  only  that  which  is 
utilised  at  the  ends  of  the  carbons  in  the  crater  and  the  white 
spot  is  useful  for  light  giving  purposes,  that  absorbed  by  the 
arc  itself  being  practically  wasted. 

X.  When  the  arc  is  lengthened,  while  the  current  is  kept 
constant,  almost  the  whole   of  the   extra   power  supplied   is   -> 
swallowed  up  by  the  carbon  mist,  and  is  practically  wasted  as 
far  as  the  creation  of  light  is  concerned.     Consequently,  more 
light  is  created,  for  a  given  power  supplied,  the  shorter  the  arc. 

XI.  Soft   carbons  give  more  light  than  hard  for  a  given 
amount  of  power,  but  they  burn  away  much  faster. 

XII.  The    most   efficient    arc    would    be    obtained    with 
infinitely  thin  carbons  and  an  infinitely  short  arc. 

XIII.  This  ideal  condition  is  most  nearly  reached  when  the 
positive  carbon  is  so  thin  for  the  current  that  the  arc  is  as 


390  THE  ELECTRIC  ARC. 

near  as  it  can  be  to  hissing  without  being  unsteady,  when 
the  negative  carbon  is  as  small  as  it  can  be,  to  burn  the 
requisite  number  of  hours,  and  when  the  length  of  the 

light  emitted 

arc  is  such  that  the  ratio  -    is    a 

power  developed    m  generator 

maximum  for  the  particular  carbons. 

XIV.  When  the  length  of  the   arc  is  constant  the   light- 
efficiency  increases  with  the  current. 

XV.  The   only  fair  method    of   comparing  two  sources  of 
light  is  to  put  each  into  the  conditions  best  suited  to  it,  and  then 


to  meunie  the  ratio  emitte<L  in  each. 

total  power  supplied 


CHAPTER    XII. 


THE  MECHANISM  OF  THE  ARC.  ITS  TRUE  RESISTANCE. 
INQUIRY  AS  TO  THE  NECESSITY  OF  A  BACK  E.M.F.  TO 
EXPLAIN  ITS  BEHAVIOUR.  WHY  CORED  CARBONS  PRODUCE 
DIFFERENT  RESULTS  FROM  SOLID  CARBONS. 

In  the  following  chapter  I  propose  to  see  how  far  the  peculiar 
behaviour  of  the  arc  might  have  been  logically  predicted  from 
the  known  conditions  of  its  existence,  viz.,  that  it  is  a  gap  in  a 
circuit  furnishing  its  own  conductor  by  the  evaporation  of  its 
own  material ;  and  to  show  that  it  is  quite  unnecessary  to 
invoke  the  aid  of  a  negative  resistance,  or  even  of  a  large  back 
E.M.F.  to  account  for  this  behaviour. 

What  happens  on  making  the  Gap. 

The  usual  explanation  given  for  the  formation  of  a  spark  or 
flash  on  opening  an  electric  circuit  is  that  it  is  caused  by  self- 
induction.  The  interesting  question  therefore  arises,  could  an 
arc  be  struck  and  maintained  if  there  were  no  self-induction 
whatever  in  the  circuit  ?  I  think  it  could.  For  the  surfaces 
of  all  solids  are  irregular,  and  therefore  all  parts  of  the  carbons 
cannot  be  separated  at  the  same  instant.  The  parts  that 
remain  in  contact  will  still  conduct  the  current,  but  the  fewer 
of  them  that  remain  the  greater  will  be  their  resistance.  The 
heat  caused  by  this  resistance  must  at  last  be  great  enough  to 
volatilise  the  carbon  at  the  remaining  points  of  contact,  and,  by 
the  time  that  no  part  of  one  carbon  is  touching  any  part  of  the 
other,  the  small  gap  will  be  full  of  carbon  vapour. 

To  explain  the  further  formation  of  the  arc,  we  must 
remember  that  when  the  separation  between  the  carbons  is  still 
greater,  all  the  material  in  the  gap,  as  I  have  explained  in 
Chapter  XI.  (p.  355), f  cannot  retain  its  high  temperature.  The 

*  The  larger  part  of  the  following  Chapter  was  embodied  in  a  Paper  en 
"  The  Mechanism  of  the  Electric  Arc,"  read  before  the  Royal  Society, 
June  20,  1901. 

t  Sec  also  p.  88  (Herzfeld). 


392  THE  ELECTKIC  ARC. 

access  of  the  cold  air  must  turn  some  of  it  into  carbon  mist  or 
fog,  and  I  have  suggested  that  the  purple  interior  portion  of 
the  image  of  the  arc  is  composed  of  such  mist,  while 
there  is  an  indication  of  a  space  between  the  mist  and  the 
positive  carbon  which  is  occupied,  I  believes  by  a  thin  film  of 
true  carbon  vapour. 

Next,  the  dissimilar  action  of  the  poles,  met  with  in  so  many 
electric  phenomena,  begins.  Instead  of  both  poles  volatilising, 
so  that  there  is  a  thin  layer  of  carbon  vapour  over  each  with  a 
mass  of  carbon  mist  between  them,  the  positive  pole  alone 
volatilises,  while  the  negative  appears  simply  to  burn  away. 

Besides  the  film  of  vapour  and  the  bulb  of  mist,  other 
volatile  materials  go  to  make  up  the  whole  substance  of  the 
arc.  The  surrounding  air  not  only  cools  the  carbon  vapour, 
but  it  unites  chemically  with  a  certain  thickness  of  the  mist, 
thus  forming  a  sheath  of  burning  gases  surrounding  both 
vapour  and  mist,  and  even  portions  of  the  solid  carbons  them- 
selves. This  sheath  of  gases  is  the  brilliant  green  flame  shown 
in  Fig.  1,  while  the  shadow  between  it  and  the  mist  (Figs.  3 
to  6)  probably  indicates  where  the  two  mingle.  There  are 
three  sorts  of  material  in  the  gap  therefore,  marking  the  three 
stages  through  which  the  vapour  is  continually  passing. 

(1)  It  starts  as  a  thin  film  of  carbon  vapour  spread  over  the 
end  of  the  positive  carbon. 

(2)  It  then  changes  into  the   mist  that  lies  between  this 
vapour  film  and  the  negative  carbon. 

(3)  Finally,  it  burns  and  forms  a  sheath  of  burning  gases 
which  encloses  not  only  the  fresh  vapour  and  mist,  but  also 
the  ends  of  the  solid  carbons  themselves. 

The  Conducting  Power  of  the  Vapour,  the  Mist  and  the  Flame. 

The  specific  resistances  of  true  vapours  are  known  to  be 
high,  therefore,  I  conclude  that  the  film  over  the  end  of  the 
positive  carbon  has  a  high  resistance,  even  though  it  be  very 
thin.  The  mist,  on  the  contrary,  is  probably  composed,  as  I 
have  already  suggested,  of  minute  solid  particles  of  carbon, 
and  must,  therefore,  I  think,  have  a  lower  specific  resistance. 
My  experiments  on  the  flame  have  shown,  on  the  other  hand, 
that  its  specific  resistance  is  so  high,  compared  with  that  of  the 
inner  purple  mist,  that  it  is  relatively  an  insulator— a  result 


THE  SOURCE  OF  THE  HEAT  OF  THE  ARC.        393 

confirming  that  obtained  by  Luggin*  in  1889.  The  current, 
therefore,  flows  through  the  vapour  and  the  mist,  but  practically 
not  at  all  through  the  sheath  of  burning  gases. 

The  production  of  the  High  Temperature  at  the  Crater. 

To  explain  the  great  production  of  heat  at  the  end  of  the 
positive  carbon,  as  well  as  the  sudden  change  of  potential  that 
is  known  to  exist  there,  it  has  been  supposed  that  a  back  E.M.F. 
of  some  35  to  40  volts  existed  at  the  junction  of  the  crater 
and  the  arc.  But  if,  as  I  suggest,  there  be  a  high  resisting 
vapour  film  in  contact  with  the  crater,  the  current  passing 
through  this  must  generate  much  heat,  and  this  heat  is  utilised 
mainly  in  continuously  forming  fresh  carbon  vapour,  to  be 
itself  turned  into  mist  and  then  into  flame.  Hence,  it  seems 
probable  that  the  high  and  constant  temperature  of  the  crater 
is  kept  up,  not  by  the  current  flowing  against  a  back  E.M.F., 
but  through  the  resistance  of  a  thin  vapour  film  at  the  surface 
of  the  crater.  In  other  words,  it  is  not  the  crater  itself  that  is 
the  source  of  the  heat  of  the  arc  but  a  thin  film  of  carbon  vapour 
in  intimate  contact  with  it. 

Why  the  End  of  the  Positive  Carbon  has  its  Particular  Shape. 

As  only  the  part  of  the  positive  carbon  that  is  in  actual 
contact  with  the  vapour  film  can  be  at  the  temperature  of 
volatilisation,  evaporation  can  only  take  place  at  that  surface ; 
and  hence,  unless  the  vapour  film  is  as  large  as  the  whole  cross 
section  of  the  positive  carbon  it  must  dig  down  into  the  carbon 
and  leave  the  surrounding  parts  unvolatilised — i.e.,  the  part  of 
the  positive  carbon  against  which  the  film  rests  must  become 
concave.  These  surrounding  parts,  however,  are  heated  suffi- 
ciently by  conduction  from  the  evaporating  surface  and  by 
the  hot  gases  surrounding  them  to  burn  away,  and  so  there 
must  be  a  race  between  volatilisation  of  the  centre  portion 
and  burning  away  of  the  edges,  which  must  in  all  cases 
determine  the  shape  of  the  surface  of  volatilisation.  When, 
all  other  things  being  equal,  the  gap  between  the  carbons  is 
small,  so  that  the  end  surface  of  each  carbon  is  well  protected 
from  the  air,  volatilisation  will  gain  over  burning,  and  the  pit 
may  become  very  deep.  When,  on  the  other  hand,  the  gap  is 

*  Wien  tiitsungabcrichtc,  Vol.  XCVIIL,  Part  I.,  Division  II.,  p.  1,233. 


394  THE  ELECTRIC  ARC. 

large,  so  that  the  air  can  easily  reach  all  parts  of  the  carbon, 
except  that  actually  covered  by  vapour,  these  parts  may  burn 
away  as  fast  as,  or  even  faster  than  the  inner  portion  is 
volatilised,  and  in  that  case  the  surface  of  volatilisation  will 
be  flat  or  even  slightly  convex.  It  is  evident,  therefore, 
from  the  very  nature  of  things,  that  this  surface  cannot  help 
being  concave  when  the  distance  between  the  carbons  is  short, 
and  flat,  or  convex  when  it  is  long.  And  this  is  true,  whether 
the  volatilisation  is  due  solely  to  a  large  back  E.M.F.,  as  some 
have  supposed,  or  to  the  resistance  of  a  thin  film  of  carbon 
vapour,  as  I  have  suggested,  or  partly  to  one  and  partly  to  the 
other. 

When  only  a  small  bit  of  the  end  of  the  positive  carbon  is 
being  volatilised,  the  outer  edge  of  the  carbon  will  not  be 
made  hot  enough  to  burn,  and  the  tip  will  remain  relatively 
blunt,  as  it  does  with  small  currents  in  Figs.  7,  8  and  9. 
When,  on  the  contrary,  the  area  of  voltilisation  is  large,  the 
edge  of  the  carbon  must  burn  away}  and  a  long  tapering  end 
will  be  found,  terminating  in  the  surface  of  volatilisation. 
The  shorter  the  arc  the  less  will  the  heat  be  able  to  escape 
between  the  carbons,  and,  consequently,  the  longer  must  be  the 
tapering  part,  as  it  is  seen  to  be  in  Figs.  7,  8  and  9  (pp.  9,  10 
and  12). 

Why  the  End  of  the  Negative   Carbon  assumes  its  Particular 

Shape. 

It  is  acknowledged  that  volatilisation  takes  place  at  the  end 
of  the  positive  carbon  only,  therefore  the  negative  carbon  must 
be  shaped  entirely  by  burning  away,  the  heat  that  raises  it  to 
burning  temperature  being  furnished  partly  by  the  mist  that 
touches  it,  and  partly  by  radiation  from  the  vapour  film  lying 
against  the  positive  carbon.  The  part  that  the  mist  rests  on  is 
protected  by  it  from  the  action  of  the  air,  and  does  not,  there- 
fore, burn  away  as  fast  as  the  rest.  At  the  same  time  it  must 
be  hotter  than  the  remainder  of  the  carbon,  and  so  the  portion 
of  the  carbon  near  it  must  burn  away  more  readily  than  the 
rest,  leaving  a  mist-covered  tip  which  will  be  longer  and 
slenderer,  because  its  sides  will  be  hotter  and  burn  away  more 
easily,  the  larger  the  crater  and  the  shorter  the  arc. 


THE  SHAPING  OF  THE  NEGATIVE  CARBON.     395 


Hence,  with  a  small  crater  and  a  long  arc  the  negative 
carbon  would  remain  fairly  flat  (a,  Fig.  125),  whereas,  as  the 
crater  became  larger,  its  action  alone  would  shape  the  negative 
carbon  as  dotted  in  (&),  and  the  extra  heating  due  to  the  mist 
would  render  it  as  shown  in  the  full  line.  With  a  short  arc,  on 
the  contrary,  a  small  crater  alone  would  produce  an  end  as 
dotted  in  (c),  while  the  combined  effect  of  the  crater  and  mist 
would  produce  the  end  outlined  by  the  full  line.  Finally,  with 
a  large  crater  and  a  short  arc  the  crater  alone  would  produce 
an  end  as  dotted  in  (d),  while  the  crater  and  mist  together 


FIG.  125. — The  Shaping  of  the  Negative  Carbon  with  Large  and  Small 
Craters  and  with  Long  and  Short  Arcs. 

would  shape  the  negative  carbon  as  given  by  the  full  line 
in  (d).  The  shapes  in  (a),  (6),  (c)  and  (d)  are  those  which  as 
shown  by  Figs.  7,  8  and  9  (pp.  9,  10  and  12)  are  actually 
acquired  by  the  negative  carbon  under  the  given  conditions. 

The  Ratio  of  the  Volume  of  the  Arc  to  its  Cross  Section  Depends  on 
the  Shapes  of  the  Carbon  Tips  as  well  as  on  the  Distance 
between  them. 

The  relation  between  the  volume  and  the  cross  section  of  the 
arc  must  depend  primarily  on  the  quantity  of  vapour  produced 
per  second  and  on  the  shapes  of  the  carbon  ends  between  and 


396  THE  ELECTRIC  ARC. 

round  which  the  resulting  mist  has  to  dispose  itself.  If  these 
ends  are  short  and  thick,  the  mist  will  be  flattened  out 
between  them,  and  its  mean  cross  section  will  be  great  com- 
pared with  its  volume.  If  the  ends  are  long  and  slender,  the 
mist  will  extend  itself  along  these  ends  and  will  have  a  small 
mean  cross  section  compared  with  its  volume.  The  thickness 
of  the  envelope  of  burning  gases,  on  the  other  hand,  does  not 
depend  primarily  on  the  quantity  of  carbon  volatilised  per 
second,  but  simply  on  the  ease  with  which  the  air  can  get  at 
the  mist  to  unite  with  it.  When  the  carbon  ends  are  thick 
they  protect  the  mist  that  is  between  them  from  the  action  of 
the  air  better  than  when  they  are  slender,  and  when  they  are 
near  together  than  when  they  are  far  apart.  Thus,  indirectly, 
the  thickness  of  the  gaseous  envelope  depends  also  on  the 
distance  between  the  carbons. 

Why  the  Area  of  the  Crater  is  not  Directly  Proportional  to  the 

Current  but  depends  also  on  the  Lenytli  of  the  Arc. 
Suppose  that  the  current  and  the  distance  between  the  ends 
of  the  carbons  have  been  kept  constant  long  enough  for  the 
arc  to  have  become  normal,  and  that  the  resistance  in  the  out- 
side circuit  is  then  suddenly  diminished.  At  the  first  instant 
the  P.D.  between  the  carbons  must  be  increased,  a  larger 
current  will  have  to  flow  through  a  vapour  film  of  the  old 
dimensions,  and,  consequently,  the  heat  developed  in  it  per 
second  will  increase.  The  temperature  of  the  film  cannot  rise, 
because  there  is  no  increase  of  pressure  ;  consequently,  it  must 
expand  and  spread  over  a  larger  area  of  solid  carbon.  The 
moment  the  film  had  expanded  in  the  slightest  degree  it  would 
begin  volatilising  carbon  from  a  part  of  the  surface  hitherto 
inactive,  and  thus  a  larger  quantity  of  vapour  per  second  would 
be  volatilised.  At  the  next  instant,  therefore,  the  quantity  of 
carbon  volatilised  per  second  would  have  increased,  and  the 
resistance  of  the  vapour  film  would  have  become  lower,  and  its 
tendency  to  expand  would  therefore  be  diminished  on  both 
accounts.  Thus,  at  each  instant  after  the  change  of  current 
the  volatilising  surface  would  increase,  but  more  and  more 
slowly,  till  its  area  was  such  that  the  heat  developed  per 
second  in  the  vapour  film  only  just  sufficed,  after  all  losses 
from  conduction,  £c.,  to  keep  up  the  volatilisation.  After 


AREAS  OF  CRATER  AND  VAPOUR  FILM.        397 

that,  the  vapour  film  would  cease  to  expand,  and  the  surface 
of  volatilisation  would  have  reached  its  maximum  area  for  the 
new  current. 

The  vapour  film,  besides  radiating  heat  in  all  directions  from 
its  free  surface,  must  lose  a  certain  extra  amount  of  heat  all 
round  its  edges  by  conduction  through  the  part  of  the  solid 
carbon  that  it  does  not  actually  touch.  The  heat  thus  lost 
must  be  subtracted  from  the  edges  of  the  part  that  it  does 
touch,  and  this  part  will  therefore  be  just  below  the  tempera- 
ture of  volatilisation  as  will  also  a  small  ring  of  the  solid 
carbon  outside  the  vapour  film.  Suppose,  for  instance,  that 
the  full  line  in  Fig.  126  is  the  part  of  the  positive  carbon  that 
is  in  contact  with  the  vapour  film,  then  the  inner  dotted  line 
will  enclose  the  area  ^ ^  that  is  actually  vola- 

tilising fresh  carbon,  ,V?*"""""*"^x\  anc^  *ne  sPace  be- 
tween the  two  dotted  ///'  Vs\  circles  will  be  at  a 
temperature  just  be  ///  \\\  low  that  of  volatili- 
sation, because  the  \\\  //'  conduction  of  heat 
from  the  edges  of  \S\  JJj  the  vapour  film  will 
bring  the  outer  circle  ^^^^^^/  UP  aQd  the  inner 
circle  down  to  a  FIG"  126  temperature  a  little 
below  that  of  the  vapour  film  itself. 
The  slightly  lower  temperature  of  the  space  between  the 
dotted  circles  would  make  it  rather  less  brilliant  than  the 
volatilising  surface,  but  it  would  still  be  very  much  more 
brilliant  than  the  remainder  of  the  positive  carbon,  so  that  it 
must  form  the  outer  circle  of  what  we  are  accustomed  to  call 
the  crater,  viz.,  the  most  brilliantly  white  part  of  that  carbon. 
The  area  of  the  crater  is  thus  rather  larger  than  the  cross- 
section  of  the  vapour  film,  while  the  actively  volatilising 
surface  is  slightly  smaller. 

When  the  carbon  vapour  proceeds  from  a  given  area  the 
cross  section  of  the  vapour  film  will  be  greater  the  more  it  is 
protected  from  the  cold  outer  air  by  the  end  of  the  positive 
carbon.  If,  for  instance,  AB,  Fig.  127,  were  the  diameter  of 
the  volatilising  surface,  the  cross  section  of  the  vapour  film 
would  be  greater  if  the  end  of  the  carbon  were  CD  than  if  it 
were  C'D',  or,  since  the  end  of  the  positive  carbon  is  thicker 
the  longer  the  arc,  the  cross  section  of  the  vapour  film  is  greater 
the  longer  the  arc.  This  film  will  also  be  able  to  keep  a  larger 


398  THE  ELECTRIC  ARC. 

ring  of  solid  carbon  at  a  temperature  just  below  that  of  volati- 
lisation when  the  end  of  the  carbon  is  CD  than  when  it  is 
C'Dr ,  therefore  the  whole  space  that  is  just  below  the  tempera- 
ture of  volatilisation,  i.e.  that  is  included  between  the  dotted 
circles  in  Fig.  126,  will  be  greater  with  a  long  arc  than  with  a 
short  one,  when  the  surface  of  volatilisation  is  the  same  size  in 
each  case.  In  other  words,  the  area  of  the  crater  increases  with 
the  length  of  the  arc  with  a  given  surface  of  volatilisation. 
Now,  I  shall  show  presently  that  in  the  normal  state  of  the  arc 
the  area  of  the  volatilising  surface  is  directly  proportional  to 
the  current,  but  is  independent  of  the  length  of  the  arc ;  it 
follows,  therefore,  that  with  a  given  constant  current  the  area 
of  the  crater  must  increase  with  the  length  of  the  arc,  as  I 
have  already  shown  it  to  do  by  actual  measurement  (p.  154). 


FIG.  127. — Positive  Carbons  having  the  same  Area  of  Volatilisation — to  the 
left  with  a  Long  Arc,  to  the  right  with  a  Short  one. 

The  area  of  the  crater  is,  then,  a  function  of  (1)  the  time  after 
a  change  has  occurred  in  either  the  current  or  the  length  (till 
the  arc  becomes  normal  again),  (2)  the  current,  and  (3)  the 
length  of  the  arc. 

The  Film  of  Vapour  in  contact  with  the  Positive  Carbon  acts 
like  a  Back  E.M.F. 

Let  a  be  that  area  of  the  film  that  uses  its  heat  in  volatilis- 
ing fresh  carbon,  and  let  x  be  the  part  of  which  the  heat  is  lost 
by  conduction,  radiation,  &c.  Then  the  whole  area  of  the  film 

is  a  +  x,  and  its  resistance  is  — - — ,  where  p  is  constant,  if  we 

a  +  x 

consider  the  thickness  of  the  film  to  be  constant.     The  heat 

#A2 
generated  per  second  in  the  film  is  proportional  to  -± — ,  and,  of 

d  +  X 

this,  only  -   —  is  used  in  volatilisation.      The  quantity  of  car- 
a  ~H  x 

bon  volatilised  per  second  is,  therefore,  proportional  to 
__a         pA2  __  apA? 
a  +  x  '  a  +  x     (a  +  a)2' 


VAPOUR  FILM  ACTING  AS  BACK  EM  F.          399 

But  the  quantity  of  carbon  volatilised  per  second  must  be  pro- 
portional to  the  surface  from  which  it  is  volatilised,  i.e.,  to  a. 

^a  -  ,  where  q  is  constant, 
'2 


or 


But 

P 

where  /  is  the  resistance  of  the  film, 


(22) 

Now  the  heat  developed  per  second  in  a  film  of  area  a  by  a 

A2 
current  A  is  proportional  to  —  ;  and,  when  all  this  heat  is  em- 

Dloyed  in  evaporating  carbon  from  the  surface  a,  the  quantity 
of  carbon  evaporated  per  second  is  proportional  to  the  area  a, 

A2 
and  also  to  the  heat  employed  in  evaporating  it,  i.e.,  to  ......  . 

CL 

We  have,  therefore, 

A  2 

a  =  —  —  ,  where  m  is  constant, 

a 

or  a  =  wA,  where  n  is  constant. 

Thus  the  area  of  the  evaporating  surface  of  the  crater  is  pro- 
portional to  the  current.  Substituting  this  value  for  a  in 
equation  (22)  we  have 


Now  we  have  seen  (p.  398)  that  x,  which  is  the  part  of  the 
vapour  film  that  loses  heat  by  conduction  at  its  edge,  must  in- 
crease as  the  arc  lengthens.  Also,  since  I  =  0  does  not  mean  that 
the  carbons  are  touching,  but  that  the  mouth  of  the  crater  and 
the  tips  of  the  negative  carbon  are  in  the  same  plane,  conduction 
at  the  edge  of  the  film  would  take  place,  even  with  no  length 
of  arc,  so  that  x  must  have  some  value,  even  when  I  =  0.  Thus 
all  we  know  about  x  and  I  is  in  accordance  with  the  equation 

x  =  v  +  wl, 
where  v  and  w  are  constants. 


400  THE  ELECTRIC  ARC. 

Let  us  assume  that  this  equation  is  true  of  x  when  I  =  0,  then 
we  have 

/=^_^£±!?), 

f    hA.  +  k  +  ml 

/-      -jr— . 
or  /_*+*!£*  (23) 

A  A 

which  is  an  equation  of  exactly  the  same  form  as  that  obtained 
by  direct  measurement.  For  equation  (6)  (p.  222)  was  found 
by  measuring  the  P.D.  between  the  positive  carbon  and  points 
in  the  mist  quite  close  to  the  crater ;  and  dividing  this  equation 
throughout  by  A  we  get 

f_  V  =  31-28     9  +  3-U 

7     A        A"     T~~ 

The  identity  of  the  two  equations  shows  that  not  only  is  no 
back  E.M.F.  at  the  crater  necessary  to  account  for  the  great 
fall  of  potential  between  it  and  the  arc,  but  that  the  film  of 
high  resistance  vapour,  whose  existence  I  have  suggested,  could 
cause  the  P.D.  between  the  positive  carbon  and  the  arc  to  vary 
exactly  as  experiment  proves  it  to  vary. 

When  A  in  equation  (23)  is  changed  to  2A,  /  becomes  less 

than  /,  which  shows  that  /  diminishes  faster  than  A  increases, 

2 

or,  in  other  words,  the  resistance  of  the  vapour  film  diminishes 
faster  than  the  current  increases. 

The  Apparent  Negative  Resistance  of  the  Arc  is  caused  by  the 
true  Positive  Resistance  Diminishing  More  Rapidly  than  the 
Current  Increases. 

It  has  been  mentioned  (p.  392)  that  the  specific  resistance 
of  the  green  flame  is  so  high  as  to  make  it,  to  all  intents  and 
purposes,  an  insulator,  so  that  nearly  the  whole  of  the  current 
flows  through  the  mist.  Consequently,  it  follows  that  the 
resistance  of  an  arc  of  given  length  must  depend  (apart  from 
the  resistance  of  the  vapour  film)  simply  on  the  cross-section 
of  the  carbon  mist,  which,  as  it  appears  purple  in  the  image  of 
the  arc,  can  easily  be  measured.  To  see  how  this  cross-section 
varies  when  the  current  is  increased  while  the  length  of  the  arc 


CROSS-SECTION  OF  ARC  MIST. 


401 


is  kept  constant,  I  have  drawn,  in  Fig.  128,  diagrams  of 
images  of  the  normal  arc,  taking  great  care  to  trace  the  exact 
limits  of  the  purple  mist  and  the  green  flame  as  accurately  as 
possible. 

The  resistance  of  the  carbon  mist  (as  distinct  from  that  of  the 
vapour  film)  may  be  defined  practically  as  being  the  resistance 
of  that  portion  of  the  mist  that  lies  between  the  two  parallel 
planes  that  pass,  the  one  through  the  mouth  of  the  crater, 
and  the  other  through  the  tip  of  the  negative  carbon. 


FIG.  128. — Diagrams  of  Arcs  and  Carbons  with  Outlines  of  Mist  and 
Flame  very  carefully  noted. 

The  mean  cross-section  of  the  mist  D2  given  in  column  (3) 
of  Table  LIII.  has  been  obtained  by  taking  the  means  of  the 
squares  of  the  three  lengths  AB,  CD  and  EF  in  Fig.  128.  The 
next  column,  giving  the  ratio  of  D2  to  the  current  A,  shows  that 
the  cross -section  of  the  mist  increases  more  rapidly  than  the 

DD 


402 


THE  ELECTRIC  ARC. 


current.  Column  5  gives  numbers  proportional  to  the  resistance 
of  the  mist,  while  columns  6  and  7  contain  numbers  proportional 
to  the  power  spent  in  the  mist,  as  obtained  by  experiment, 
and  from  the  equation  to  be  subsequently  referred  to. 

The  mist  carries  practically  the  whole  of  the  current,  and, 
since  D2  increases  more  rapidly  than  A  (column  4),  it  follows 
that  in  the  normal  arc  the  resistance  of  the  mist  diminishes 
more  rapidly  than  the  current  increases.  But  I  have  shown 
(p.  400)  that  the  resistance  of  the  vapour  film  also  diminishes 
faster  than  the  current  increases.  Hence,  the  whole  resistance 
of  the  normal  arc  diminishes  more  rapidly  than  the  current 
increases,  and  for  this  reason  the  P.D.  required  to  send  the 

Table  LIU.  Mean  Squares  of  Diameters  of  Mist  ivith  corre- 
sponding Currents  and  P.Ds.  between  the  Carbons.  Numbers 
proportional  to  Resistance  of  Mist  and  to  Power  expended 
in  Mist. 

Normal  Arc.     Constant  Length  of  Arc,  2mm. 
Solid  Carbons :  Positive,  llmm.  ;  negative,  9mm. 


I 

A           V 

) 
1 

D2 

sq.  mm. 

D2 
A 

•^ 
D2 

A^ 
D2 
experiment. 

A2 
D2 
from  equation. 

4          51-7 
6     ;      49-0 
8'    1      48-0 
10          47-0 
12     I      45-7 
14     !      45-1 

4'8 
9-8 
16-2 
23-4 
34-9 
41-2 

1-20 
1-63 
2-02 
2-34 
2-91 
2-94 

0-208 
0-102 
0-061 
0-C43 
0-029 
0-024 

3-33 
3-67 
3-95 
4-27 
4-13 
4-76 

3-4 
3-68 
3-95 
4-22 
4-49 
4-76 

current  through  this  resistance  must  also  diminish  as  the  current 
increases.  Thus,  if,  in  the  normal  arc,  SA  be  an  added  incre- 
ment of  current  and  8V  the  accompanying  increment  of  P.D., 

8V 

—  must  have  a  negative  value,  even  although  the  resistance  of 

the  arc  is  positive,  simply  because  that  resistance  diminishes 
faster  than  the  current  increases. 

There  is  Nothing  to  Show   that  the  P.D.  between  the  Carbons 
Divided  by  the  Current  is  not  the  True  Resistance  of  the  Arc. 

Fig.  129  shows  that^the  curve  connecting  the  values  of—, 
given  in  the  sixth  column  of  Table  LIU.,  with  those  of  the 


RESISTANCE  OF  ARC  MIST.  403 

current,  in  the  first  column,  is  a  straight  line,  having  the  equation 


so  that,  for  a  normal  arc  of  given  length,  the  power  expended 
in  the  carbon  mist  is  proportional  to  a  constant  plus  a  term 
which  varies  directly  with  the  current.  Dividing  by  A2  we 
obtain  m,  the  resistance  of  the  mist, 

0-136     2-86 

m  =s + . 

A          A2 

Now,  let  us  suppose  that,  for  a  given  current,  the  resistance 
of  the  mist  is  directly  proportional  to  the  length,  ?,  of  the  arc, 
then  the  equation  for  m  must  take  the  form : — 


w=    -+TT7 


?,  ••»    4-0 


3-0 


10 


14 


0246 

Current  in  Amperes. 
FIG.  129.—  Curve  connecting  the  Power  expended  in  the  Mist  with  the 

Current,  for  a  Constant  Length  of  Arc  of  2mm. 
Solid  Carbons  :   Positive,  llmm.  ;   negative,  9mm. 

Combining  this  with  /,  the  resistance  of  the  vapour  film,  in 
equation  (23),  we  have  for  the  total  resistance  of  the  normal 
arc  an  expression  of  the  form 


a  form  of  equation  exactly  similar  to  (5),  p.  190,  in  which  the 
apparent  resistance  of  the  arc  was  found  by  dividing  the  P.D. 

DD2 


404  THE  ELECTRIC  ARC. 

between  the  carbons  by  the  current.  Thus  the  law  of  variation 
of  the  resistance  of  the  arc  is  identical,  whether  it  is  obtained 
from  direct  measurements  of  the  cross-sections  of  the  vapour 
film  and  the  mist,  or  by  dividing  the  observed  P.D.  between 
the  carbons  by  the  current.  It  may  well  be,  therefore,  that, 
instead  of  an  arc  consisting  of  a  circuit  of  low  resistance  com- 
bined with  a  large  back  E.M.F.,  its  apparent  resistance — i.e., 
the  ratio  of  V  to  A — is  its  true  resistance  ;  or  that,  if  there  is 
any  back  E.M.F.  at  all,  it  is  very  much  smaller  than  has 
hitherto  been  supposed. 

Both  the  Resistance  of  the  Arc  and  the  P.D.  between  the  Carbons 
Depend,  not  only  on  the  Current  and  the  Length,  but  also  on 
II ow  Lately  a  Change  has  been  'made  in  Either,  and  on 
What  that  Change  was. 

The  whole  resistance  of  the  arc  depends  on  the  cross-sections 
of  the  vapour  film  and  the  mist,  and  on  the  distance  between 
the  carbons.  Now,  we  have  seen  (p.  396)  that  when  the  P.D. 
between  the  carbons  is  changed — increased,  say — the  first 
result  must  be  an  increase  of  current,  while  the  second  is  a 
corresponding  increase  in  the  cross-sections  of  the  vapour  film 
and  the  mist,  causing  a  diminution  of  the  resistance,  and,  con- 
sequently, of  the  P.D.  between  the  carbons.  Thirdly,  if  the 
new  current  is  kept  constant  long  enough,  the  ends  of  the 
carbons  burn  away  to  longer  points,  allowing  the  mist  to 
extend  further  along  their  sides,  and  so  to  take  a  smaller  cross- 
section,  so  that  both  the  resistance  and  the  P.D.  increase 
again,  although  they  never  reach  such  high  values  as  they  had 
with  the  smaller  current. 

Fig.  130  is  useful,  as  showing  at  a  glance  how  the  resistance 
and  the  P.D.  depend  upon  the  time  that  has  elapsed  after  a 
change  of  current,  when  the  current  is  kept  constant  after 
the  change.  When  the  arc  is  normal  in  the  first  instance 
AB,  A'B'  and  A"B"  represent  the  curves  connecting  the  P.D., 
the  current  and  the  true  resistance  of  the  arc  respectively 
with  the  time.  When  the  P.D.  is  increased  from  B  to  C,  say, 
the  resistance  does  not  alter  at  the  first  instant,  but  the 
current  rises  to  C',  and  it  is  then  kept  constant  at  C'.  Next,  the 
surface  of  volatilisation  increases  in  area,  so  that  the  resistance 
falls  to  D",  and  the  P.D.  consequently  falls  to  D.  After  this 


TIME-CHANGES  OF  P.V.  CURRENT  &  RESISTANCE.  405 


the  carbons  begin  to  grow  longer  points,  the  cross-section  of 
the  mist  diminishes,  the  resistance  therefore  increases  to  E", 
and  the  P.D.  with  it  to  E.  The  arc  has  now  become  normal 
again,  so  that  the  curves  are  all  now  parallel  straight  lines,  the 
current  higher  than  before,  and  the  P.D.  and  resistance  lower. 
Thus  any  alteration  that  is  made  and  maintained  in  the  arc 
sets  up  a  series  of  changes  in  its  resistance  and,  consequently, 
in  the  P.D.  between  the  carbons,  that  cease  only  when  the  arc 


PD. 


Current- 


Resi! 


Zero  Line  of  Resistance,  Current,  and  P.D. 
Time. 

FIG.  130. — Simultaneous  Time-Changes  of  P.D.,  Current  and  Resistance. 

becomes  normal  again.  In  other  words,  when  an  arc  of  given 
length,  with  a  given  current  flowing,  exists  between  given 
carbons,  neither  the  resistance  nor  the  P.D.  between  the 
carbons  has  any  definite  value,  except  when  the  arc  is  and 
remains  normal.  In  all  other  cases,  each  varies,  within  certain 
limits,  according  to  the  time  that  has  elapsed  since  either  the 
current  or  the  length  was  altered,  and  according  to  what 


06  THE  ELECTRIC  ARC. 

change  was  then  made.  Experimental  proof  of  the  above- 
mentioned  alterations  in  the  P.D.,  corresponding  with  current 
changes,  has  already  been  given  in  Chapter  III.,  Figs.  36 
and  37,  with  the  exception  of  the  first  change  of  P.D.  in  the 
same  direction  as  the  change  of  current.  This  was  so  quick 
that  it  was  over,  before  it  could  influence  the  voltmeter,  in 
every  case  but  when  both  carbons  were  cored.  The  reason 
why  will  appear  later.  These  changes  have  an  important 
bearing,  which  we  will  now  examine,  on  the  question  of 
measuring  the  resistance  of  the  arc  by  means  of  a  small  super- 
imposed alternating  current. 

This  method  has  been  employed  by  many  experimenters,  but 
the  results  obtained  have  not  shared  the  similarity  of  the 
methods;  for  while  Von  Lang  and  Arons  found,  in  1887,  that 
the  arc  had  a  positive  resistance,  Messrs.  Frith  and  Rodgers, 
in  1896,  found  that  it  had  a  negative  one,  with  solid  carbons. 
We  shall  now  see  the  reason  of  this  disparity,  and  first  it  may  be 
well  to  recall  shortly  the  reasoning  on  which  the  method  is  based. 

The  equation 


may  be  taken  to  represent  the  connection  between  the  P.D. 
between  the  carbons,  the  current  and  the  length  of  the  arc, 
whether  it  has  a  variable  E.M.F.,  a  constant  E.M.F.,  or  none 
at  all.  For,  in  the  first  case,  E  will  be  variable,  in  the  second 
constant  and  in  the  third  zero.  In  any  case 

(7V 

_  r—  rt-» 

dA 

when  such  a  small  quick  change  is  made  in  V  and  A  that 
neither  E  nor  r  is  made  to  vary  by  it. 

Instead  of  a  single  small  quick  change  of  current,  the 
experimenters  superimposed  a  small  alternating  current  on  the 
direct  current  of  the  arc,  and  measured  the  average  value 

8V 
of  —  ,  or  its  equivalent.     Obviously,  if  the  alternating  current 

left  the  resistance  and  any  back  E.M.F.  that  might  exist  in  the 
arc  unaffected,  this  was  a  true  measure  of  the  resistance  of  the 
arc.  But  if  the  alternating  current  changed  both  or  either  of 
these,  then,  instead  of  being  equal  to  r  we  should  have 


THE  VALUE  OF       .  407 

oA 

if  there  is  a  back  E.M.F.,  and  if  both  it  and  the  resistance 
varied  with  the  alternating  current  ;  we  should  have 

dV_        dE 
c/A       +  dK' 

if  there  is  a  back  E.M.F.  and  if  it  alone  varied,  and 


if  the  back  E.M.F.  is  either  non-existent  or  constant,  and  the 
resistance  alone  varied. 

None  of  the  experimenters,  as  far  as  I  am  aware,  applied  any 
but  a  few  imperfect  tests  to  see  whether  the  alternating 
currents  they  employed  affected  the  resistance  of  the  arc  or  not, 
and  it  was,  I  believe,  because  the  resistance  ivas  affected,  in 
every  case,  that  such  diverse  results  were  obtained.  The  low 
frequency  of  the  alternations  was  the  probable  source  of  error, 
for  I  shall  now  show  that,  with  a  given  root  mean  square  value 

SV 
of  the  alternating  current,  the  average  value  of  —  varies,  not 

oA 

only  in  magnitude,  but  even  in  sign,  with  its  frequency. 

Effect  of  the  Frequency  of  the  Superimposed  Alternating  Current 

8V 

on  the  Value  and  Sign  of  —  . 
oJ\. 

In  dealing  with  a  superimposed  alternating  current  there 
is,  of  course,  no  sudden  increase  or  diminution  of  current 
such  as  was  dealt  with  in  Fig.  130,  everything  is  gradual. 
The  three  changes  of  P.D.  do  not,  therefore,  act  separately. 
At  any  moment  —  when  the  current  is  increasing,  say  —  the 
P.D.  has  a  tendency  to  rise  on  account  of  the  latest 
increase  of  current,  to  fall  on  account  of  the  diminution  of 
resistance  due  to  the  last  increase  but  one,  and  to  rise  on 
account  of  the  re-shaping  of  the  carbons  following  the  last 
increase  but  two.  If  the  frequency  of  the  alternating  current 
is  very  low  indeed,  so  that  the  current  changes  very  slowly,  all 
three  of  these  tendencies  will  be  in  force  at  each  moment,  and 
the  actual  change  of  P.D.  will  be  the  resultant  of  the  three. 
If  the  frequency  is  so  high  that  the  shapes  of  the  carbons  never 
change  at  all,  but  so  low  that  the  area  of  the  volatilising 
surface  can  alter,  only  the  first  two  tendencies  will  be  operative  ; 


408 


THE  ELECTRIC  ARC. 


while,  if  the  frequency  is  so  high  that  the  area  of  the 
volatilising  surface  remains  constant,  the  resistance  of  the  arc 
will  not  alter  at  all,  the  current  and  P.D.  will  increase  and 
diminish  together  and  proportionately,  and,  unless  the  arc  con- 
tains a  variable  E.M.F.  which  is  influenced  by  the  changes  of 

OTT 

current,  —  will  measure  the  true  resistance  of  the  arc. 


Line  of  Mean 
R  D.  and  Current  ^ 


Time 

FIG.  131. — Curves  showing  the  effect  of  the  Frequency  of  an  Alternating 
Current  Superimposed  on  a  Direct  Current  Arc  on  the  Simultaneous  Time- 
Changes  of  P.D.  and  Current. 

The  influence  of  the  frequency  of  the  alternating  current  on 

$\\7 

the  magnitude  and  sign  of-—  is  traced  in  Fig.  131,  where  the 

Ozx 

zero  lines  of  P.D.  and  current  are  drawn  at  such  a  distance 
apart  that  the  mean  P.D.  line  and  the  mean  current  line  are 
represented  by  the  same  horizontal  line  OPR.  PR  repre- 
sents the  time  occupied  by  one  complete  alternation,  whatever 


VARIATION  OF  |?  WITH  FREQUENCY.  409 

that  time  may  be.  If,  for  instance,  the  frequency  is  50 
complete  alternations  per  second,  PR  represents  -\jth  of  a 
second  ;  if  the  frequency  is  5,000,  PR  represents  5^-Vo^h  of 
a  second.  PSQTR  represents  the  time  change  of  current  with 
any  frequency.  When  the  alternations  are  so  slow  that  the 
are  remains  normal  the  change  of  P.D.,  SV,  for  a  given  small 
change  of  current,  SW,  say,  is  the  resultant  of  three  such 
changes  as  BC,  CD  and  DE  in  Fig.  130,  and  it  is  in  the  opposite 

direction  from  the  change  of  current.    The  P.D.  time  curve  is, 

£V 
therefore,  something  like  PXQYR  (Fig.  131),  and  ~  is  the 

ZX 

mean  of  such  ratios  as  -  — — . 
o  W 

When  the  frequency  is  so  raised  that  the  carbons  never 
have  time  to  alter  their  shapes  completely  before  the  current 
changes,  the  third  component  DE  (Fig.  130)  is  smaller  than  with 

the  normal  arc,  so  that  SV  is  greater,  and  — .  must,  therefore, 

oA. 

have  a  larger  negative  value  than  when  the  arc  is  normal, 
so  that  PX1QY1R  might  be  the  P.D.  time  curve  in  this  case. 

When  the  frequency  was  so  high  that  the  carbons  never 
altered  their  shapes  at  all,  but  the  volatilising  surface  under- 
went the  maximum  alteration,  the  third  component  (DE,  Fig. 
130)  would  be  absent  altogether,  and  therefore  SV  would  under- 
go the  greatest  change  it  was  susceptible  of  in  the  opposite 
direction  to  the  change  of  current.  PX2QY2R  is  then  the  P.D. 

OTT 

time  curve,  —  has  then  its  maximum  negative  value,  and  is 

Z  X 

the  mean  of  such  ratios  as  -  _i_ ?. 

With  a  further  increase  of  frequency,  the  area  of  the 
volatilising  surface  would  never  have  time  to  change  completely, 
so  that  8V  would  be  the  resultant  of  two  such  changes  as  BO 

CNTT 

and  CF,  say  (Fig.  130).  ^— would  therefore  be  smaller  than  with 
oA. 

the  lower  frequency  last  mentioned,  and  the  P.D.  time  curve 
might  again  be  PXjQYjR,  or  it  might  be  PX3QY3R,  if  the 
frequency  were  high  enough.  When  the  frequency  was  so  great 
that  the  two  P.Ds.  BC  and  CF  (Fig.  130)  were  exactly  equal, 
the  P.D.  would  not  alter  at  all  when  the  current  was  changed, 

SV 

—would  be  zero,  and  the  straight  line  PQR  would  be  the  P.D. 


410  THE  ELECTRIC  ARC. 

time  curve.  When  the  frequency  was  further  increased,  the 
change  of  P.D.  would  be  the  resultant  of  two  such  changes  as  BC, 
CG  only  (Fig.  130);  the  total  change  of  P.D.  would,  therefore, 
be  in  the  same  direction  as  the  change  of  current,  the  P.D. 

time  curve  would  be  like  PX4QY4R,  and  ~  would  be  +|£4. 

Finally,  when  the  frequency  was  so  great  that  the  area  of  the 
volatilising  surface  never  altered  at  all,  the  change  of  P.D.  would 
be  BC  alone  (Fig.  130),  the  P.D.  time  curve  would  be  PX5QY5R, 

OTT  rr   -\r 

SV  would  be  Z.X-,  and  — -  =  +  -A*  would  measure  the  true 

O.TX  1^  VV 

resistance  of  the  arc,  even  if  there  is  a  back  E.M.F.  in  the 
arc,  unless  that  back  E.M.F.  varies  with  the  current. 

Thus,  by  applying  the  same  alternating  current,  but  with 

6V 
different  frequencies,  to  a  direct  current  arc,  ^  can  be  made 

oA 

to  have  any  value  from  a  fairly  large  negative  value  to  the 
positive  value  which  is  the  true  resistance.  It  is  easy  to  see 
therefore,  how  different  experimenters  might  get  very  different 
values  and  even  different  signs  for  the  resistance  of  the  arc, 
when  they  measuerd  it  by  means  of  a  superimposed  alternating 
current;  and  Fig.  131  shows  the  imperative  necessity  of  some 
rigorous  proof  that  the  alternating  current  has  not  affected  the 
resistance  of  the  arc  before  any  such  measurements  can  be 
accepted  as  final,  I  shall  presently  show  how  such  a  proof  can 
be  obtained;  but  first  it  will  be  interesting  to  see  how,  with 
an  arc  of  given  length,  and  with  a  given  current  flowing,  the 

8V 

value  of  —  is  connected  with  the  frequency  of  the  alter- 
nating current,  and  what  sort  of  frequency  is  required  in 
order  that  the  resistance  of  the  arc  shall  not  be  affected  by 
this  current. 

K\T 

To  find  the  Curve  Connecting  -—  with  the  Frequency  of  the  Super- 
imposed Alternating  Current,  and  to  see  with  what  Frequency 

—  Measures  the  True  Resistance  of  the  Arc. 
oA 

Take  an  arc  of  2mm,  with  a  direct  current  of  10  amperes 
flowing. 

For  the  arc  to  remain  normal,  when  the  small  alternating 
current  is  superimposed  on  it,  the  frequency  must  be  practically 


CONNECTION  BETWEEN  —  AND  FREQUENCY.    411 

cA 

zero,  for  each  alternation  must  take  many  seconds  instead  of 
only  a  small  fraction  of  a  second.  Now,  differentiating 
equation  (3)  (p.  184)  we  find  that  with  the  normal  arc  and  with 
solid  Apostle  carbons 

SV=  _  11-66  +  10-54* 

8A  "A* 

=  -  0-33, 
when  1  =  2  and  A  =  10. 

8V 

The  first  point  on  the  curve  connecting  —  -.  with  the  fre- 

O.A. 

quency  of  the  alternating  current  has,  therefore,  the  co- 
ordinates 0  and  -0-33  (A,  Fig.  132). 

8V 

The  value  found  for  -  —  by  Messrs.  Frith  and  Rodgera  *  with 
oA    ' 

the  same  carbons,  direct  current,  and  P.D,  was  about  -  0*8i 
more  than  double  the  normal  value  —  which  shows  that  the 
alternating  current  they  superimposed  was  making  the  resis- 
tance of  the  arc  vary  so  that  the  P.D.  followed  some  such  curve 
as  PXxQY^  or  PX2QY2R  (Fig.  131).  They  also  found  that 
varying  the  frequency  from  7  to  250  complete  alternations 
made  no  difference  in  the  value  they  obtained.  Therefore,  the 

8V 
curve  connecting  —^  with  the  frequency  must  fall  steeply  from 

oA. 

A,  the  point  of  no  frequency,  to  B,  the  point  for  a  frequency  of 
7,  and  must  be  practically  horizontal  from  B  to  C.  Hence, 
Messrs.  Frith  and  Kodgera'  observations  cover  the  portion  BC 
of  the  curve  in  Fig.  132. 

The  next  point,  D,  is  obtained  from  Mr.  Duddell's  work.  In 
his  remarkable  Paper  f  on  "  Kapid  Variations  in  the  Current 
through  the  Direct-Current  Arc,"  he  said  :  —  "  I  tried  to  record 
the  transient  rise  in  P.D.  for  the  solid  arc  by  means  of  an 
oscillograph,  the  sudden  increase  of  the  current  being  obtained 
by  discharging  a  condenser  through  the  arc.  This  experiment 
was  successful,  and  a  transient  rise  in  P.D.  was  observed,  the 
P.D.  and  current  increasing  together,  but  only  for  about 


OTT 

second."    It  is  clear  from  this  that  _  must  at  least  begin  to  be 

oA. 

positive  with  a  frequency  of  2,500  complete  alternations,  and 

*  Phil.  Mag.,  1896,  Vol.  XLII.,  Plate  5. 

f  Journal  of  the  Institution  of  Electrical  Engineers,  Vol.  XXX.,  p.  232. 


412 


THE  ELECTRIC  AUC. 


vs 

- 


CONNECTION  BETWEEN         AND  FREQUENCY.    413 

0A 

D,  where  OD  =  2,500,  may  be  taken  to  be  the  point  near  which 

8V 

—  -  changes  its  sign. 

oA. 

To  the  right  of  D  the  curve  must  continue  to  rise,  as 
indicated  in  Fig.  132,  more  and  more  slowly,  as  it  approaches 
the  horizontal  line  whose  distance  from  the  axis  of  frequency 

8V 
represents  the  value  of  ^—  that  is  the  true  resistance  of  the 

oA 

arc.  The  curve  must  finally  become  asymptotic  to  this  line, 
since  when  once  a  frequency  is  nearly  reached  with  which  the 
alternating  current  does  not  practically  affect  the  resistance  of 
the  arc,  increasing  the  frequency  will  not  alter  the  value  of 
SV 
8A* 

Equation  (3)  (p.  184)  shows  that  the  resistance  of  the  par- 
ticular 2mm.  10  ampere  normal  arc  under  discussion  cannot  be 
greater  than  4-63  ohms,  nor  less  than  0-62  ohms  ;  for  if  there  is 
no  back  E.M.F. 


38-88  +  2  x  2-07  ,  1  1-66  +  10-54  x  2 

-ur  4oo-     =4'68' 

and  if  there  is  the  largest  possible  back  E.M.F.,  viz., 
K58-88  4-  —  1—  J  volts  (for  it  is  impossible  to  imagine  that 

terms  involving  the  length  of  the  arc  can  belong  to  a  back 
E.M.F.),  then 

r_  2-07x2     10-54x2 
10  100 

Thus  the  curve  cannot  rise  higher  than  the  horizontal  line  —  - 

dV  ^A 

=  4*63,  and  it  must  rise  at  least  as  high  as  Tr  =  0'62.     Conse- 

quently, as  the  lower  curve  in  Fig.  132  shows,  the  true  resis- 
tance of  this  particular  arc  could  not  be  measured  with  a 
superimposed  alternating  current  having  a  frequency  of  less 
than  at  least  7,000  per  second,  even  if  there  were  a  back 
E.M.F.  as  great  as  40  volts.  And  if,  as  I  have  suggested,  the 
back  E.M.F.  is  zero,  or  at  least  very  much  smaller  than  40 
volts,  the  frequency  would  have  to  be  many  times  as  high  for 

cZV 

—  -  to  be  on  the  horizontal  part  of  the  curve,  i.e.,  for  the  alter- 

d/A. 

nating  current  not  to  alter  the  resistance  of  the  arc. 


414  THE  ELECTRIC  ARC. 

The  Form  of  the  P. D. -Time  Curve  indicates  whether  the  Resis- 
tance of  the  Arc  is  A/ected  by  the  Superimposed  Alternating 
Current  or  not. 

The  final  test  as  to  the  frequency  being  high  enough  not  to 
affect  the  resistance  of  the  arc  must,  of  course,  be  the  finding 
of  two  frequencies  with  the  same  root  mean  square  value  of 
the  alternating  current,  but  differing  by  many  thousands  of 

SV 
alternations  per  second  that  would  give  the  same  value  of   — . 

5V  5A 

This  would  show  that  the  horizontal  part  of  the-g^  frequency 

curve  had  been  found. 

A  very  good  first  test,  however,  is  furnished  by  the  curve 
connecting  the  P.D.  between  the  carbons  with  the  time,  or 
with  the  angle  of  the  alternating  wave.  For  this  curve  is 
unsymmetrical  with  respect  to  the  corresponding  current  curve 
when  the  resistance  is  affected,  for  the  following  reasons  : — 

I  have  shown  that  the  change  in  the  area  of  the  volatilising 
surface  of  the  crater  that  is  due  to  any  change  of  current 
follows  after  the  change  of  current,  and  requires  time  for  its 
completion.  If,  therefore,  a  superimposed  alternating  current 
is  affecting  the  resistance  of  a  direct-current  arc  the  P.D. 
required  for  any  given  current  must  be  higher  when  the 
current  is  increasing  than  when  it  is  diminishing.  A  current 
of  10  amperes,  for  instance,  would  require  a  higher  P.D.  when 
it  came  after  9  and  before  11  amperes  than  when  it  came  after 
11  and  before  9  amperes,  because  in  the  first  case  it  would  be 
flowing  through  an  arc  of  which  the  cross-section  had  been 
made  by  some  current  less,  and  in  the  second  by  some  current 
greater  than  10  amperes. 

I  have  applied  this  test,  with  very  satisfactory  results,  to 
some  curves  made  from  experiments  in  which  it  is  quite  certain 
that  the  alternating  currents  must  have  affected  the  resistance 
of  the  arcs,  because  they  had  frequencies  of  only  47  and  115 
alternations  per  second  respectively. 

The  experiments  formed  part  of  a  valuable  series  carried  ou 
in  1896  by  Messrs.  Ray  and  Watlington,  two  students  at  the 
Central  Technical  College,  in  continuation  of  the  researches  of 
Messrs.  Frith  and  Rodgers.     The  carbons  were  solid,  and  the 
direct-current  normal  arc  carried  a  current  of  10  amperes  with 


TEST  FOR  ALT.  CURRENT  AFFECTING  RESISTANCE.  415 

a  P.D.  of  45  volts.  Various  P.Ds,,  with  their  corresponding 
currents  taken  from  the  curves,  are  given  in  Table  LIV.,  in 
which  the  columns  headed  V4  are  the  P.Ds.  with  increasing 
currents,  and  those  headed  Vd  with  diminishing  currents; 
while  Vg  and  Vz  belong  to  the  smallest  and  largest  currents 
respectively. 

It  may  be  seen  at  a  glance  that  in  every  single  instance  the 
P.D.  for  the  same  current  is  higher  when  the  current  is 
increasing  than  when  it  is  diminishing.  For  instance,  with  the 
lower  frequency  the  P.D.  corresponding  with  a  current  of 


Table  LIV. — Corresponding  Currents  and  P.Ds.  with  Small 
Alternating  Current  Superimposed  on  Direct  Current  of 
10  Amperes  in  the  Arc. 

P.  D.  with  Direct  Current  alone  45  volts. 
Solid  Apostle  Carbons:  Positive,  llmm.;  negative,  9mm. 


Frequency  47. 


A 

V8 

Vt 

V; 

Vd 

A 

vs 

v«' 

V, 

vd 

8-425 
9-0 
9-5 

10-0 

10-5 
11-0 
11-5 
12-0 

45-6 

: 

44-8 
44-2 
43-7 
43-1 
42-4 
42-0 
41-7 

4*4-0 
43-3 
42-8 
42-1 
41-8 
41-4 
41-2 

8-65 
9-0 
9-5 

10-0 

10-5 
11-0 
11-25 

46 

45*6 
45-2 
44-6 
43-9 
43-2 

• 

. 

42*2 

44:9 
44-2 
43-5 
42-9 
42-0 

12-25 

41-4 

... 

! 

Frequency  115. 


11  amperes  is  42  (4  volts  when  the  current  is  increasing,  and 
only  41-8  volts  when  it  is  diminishing.  And  with  the  higher 
frequency  it  is  43 '2  volts  with  increasing  current  and  only 
42-0  with  a  falling  current.  Hence,  we  are  supplied  with  a 
very  simple  test  as  to  whether  the  superimposed  alternating 
current  changes  the  resistance  of  the  arc  or  not.  It  is  only 
necessary  to  take  the  wave  forms  of  P.D.  and  current  by  means 
of  an  oscillograph,  and  to  observe  whether  the  P.D.  corre- 
sponding with  each  current  is  the  same  whether  the  current 
is  increasing  or  diminishing.  If  the  two  P.D.'s  are  different  the 
resistance  is  being  altered,  if  they  are  alike  it  is  not. 


416  THE  ELECTRIC  ARC. 

How  to  ascertain  with  Certainty  whether  there  is  a  Constant  or 
a  Variable  Back  E.M.F.  in  the  Arc  or  None,  and  how  to 
find  the  True  Back  E.M.F.,  if  there  is  One. 

Returning  to  the  equation 


dV     rfE  A  dr 

if  both  E  and  r  vary  —  =  -^  +  r  4-  A—  ; 
7   dA     dA  dA 

and 

V       A^      F       A^E       A2^r 
V  —  A-—  -  -  JL  —  A——  —  A  —  —  . 

dA  dA.         dA 

If  the  alternating  current  with  which  —  -  is  measured  is  of 

dA 

such  high  frequency  that  it  does  not  alter  the  resistance  of 
the  arc,  and  if,  also,  the  back  E.M.F.  is  constant,  or,  being 
variable,  the  alternating  current  is  too  small  to  affect  it,  then 


To  see  whether  the  arc  has  any  back  E.M.F.  at  all,  there- 

fore, it  is  only  necessary  to  measure  —  —  with  a  superimposed 

dA. 

alternating  current  of  a  frequency  that  has  been  found  not  to 

affect  its  resistance,   and  to  subtract  A—-  from  V.     If  the 

dA 

result  is  zero  the  arc  has  no  back  E.M.F.     If  it  is  not  zero, 

—must  be  measured  in  the  same  way  for  other  arcs  differing 
dA  ^y 

widely  in  current  and  length.  If  all  the  values  of  V-A-rr 
thus  obtained  are  equal  or  nearly  so,  the  arc  has  a  constant 

back  E.M.F.  which  is  equal  to  this  value.     If  V  -  A—  is  not 

dA 

the  same  for  all  the  arcs,  but  varies  according  to  some  definite 
law,  then  there  is  a  variable  back  E.M.F.  in  the  arc  which 
may  or  may  not  be  affected  by  the  alternating  current  used  to 

SV 
measure  err  . 

SA  SV 

Suppose,  for  instance,  that  two  measuements  of  g-r    were 

made,  using  the  same  direct  current  and  length  of  arc,  but 
different  alternating  currents.  If  one  of  the  alternating 
currents  had  a  root  mean  square  value  equal  to  1  per  cent,  of 


EFFECT  OF  CORES  ON  RESISTANCE.  417 

the  direct  current  and  the  other  a  value  equal  to  5  per  cent., 
one  would  be  five  times  as  great  as  the  other,  and  yet  both 
would  be  small  compared  with  the  direct  current.  It  wouldj 
of  course,  be  possible  to  make  the  frequency  of  each  of  these 
currents  so  great  that  the  resistances  of  the  arcs  to  which  they 
were  applied  were  not  altered  by  them.  Yet  it  would  not 

necessarily  follow  that  when  this  had  been  done  the  two  values 

K\T 
of  —L  thus  obtained  would  be  equal.     For  the  back  E.M.F. 

SA 

might  vary,  not  with  the  frequency  of  the  alternating  current, 
but  with  its  magnitude.  If,  therefore,  it  were  found  that 

E  was   variable  it  would  be  necessary  to  measure  — -  with 

CeA, 

smaller  and  smaller  alternating  currents  till  two  were  found 
which,  while  differing  considerably  from  one  another,  gave 

the  same  value  of  —^-.     Only  a  value  obtained  in  this  way 
ctA. 

could  be  accepted  as  measuring  the  true  resistance  of  the  arc, 

and  V  -  A —  would  then  be  the  true  back  E.M.F.  of  the  same  arc. 
dA. 

THE  CHANGES  INTRODUCED  INTO  THE  EESISTANCE  OP  THE  ARC 
BY  THE  USE  OF  CORED  CARBONS. 

The  preceding  applies  to  all  carbon  arcs.  Next  let  us  consider 
the  explanation  of  the  marked  effects  produced  by  introducing 
a  core  into  either  or  both  carbons.  These  are,  first,  those  such 
as  Prof.  Ayrton  published  at  Chicago  in  1893,  viz.: — 

(1)  The  P.D.  between  the  carbons  is  always  lower,  for  a 
given  current  and  length  of  arc,  when  either  or  both  of  the 
carbons  are  cored  than  when  both  are  solid. 

(2)  With  a  constant  length  of  arc  and  increasing  current, 
the  P.D.,  which  diminishes  continuously  when  both  carbons 
are  solid,  either  diminishes  less  than  with  solid  carbons,  when 
the  positive   is  cored,    or,   after   diminishing   to  a  minimum 
remains  constant  over  a  wide  range  of  current,  or  increases 
again. 

(3)  It  requires  a  larger  current,  with  the  same  length  of  arc, 
to  make  the  arc  hiss  when  the  positive  carbon  is  cored  than 
when  both  are  solid. 

Secondly,  there  are  the  facts  connected  with  the  influence 
of  cores  on  the  small  change  of  P.D.  accompanying  a  small 


418  THE  ELECTRIC  ARC. 

change  of  current,  to  which  attention  was  first  called  by  Messrs. 
Frith  and  Rodgers  in  1896  (see  pp.  76-81).*  These  facts,  which 
were  physically  correct,  although  they  were  wrongly  interpreted 
at  the  time,  are  embodied  in  the  following  wider  generalisations, 
which  are  deduced  from  experiments,  presently  to  be  described, 
combined  with  theoretical  considerations  : — 

(1)  When,  on  a  direct  current  arc,  an  alternating  current  is 
superimposed  which  is  such  that  the  resistance  of  the  arc  is 

altered  by  it,  the  average  value  of  —  is  always  more  positive! 

oA 

when  either  carbon  is  cored  than  when  both  are  solid,  and 
most  positive  of  all  when  both  are  cored,  all  other  things  being 

equal. 

3V 

(2)  The  frequency  of  the  alternating  current  that  makes  — . 

oA 

begin  to  have  a  positive  value  is  lower  when  either  carbon  is 
cored  than  when  both  are  solid,  and  lowest  when  both  are  cored. 

SV 

(3)  The  value  of  ^-,  with  a  given  root  mean  square  value  of 

the  superimposed  alternating  current,  depends  not  only  on  the 
nature  of  the  carbons  and  on  the  frequency  of  that  current, 
but  also  on  the  magnitude  of  the  direct  current,  and  on  the 
length  of  the  arc. 

There  are  two  ways  in  which  the  P.D.  between  the  carbons 
may  be  lowered  by  the  core  :  (1)  by  an  increase  in  the  cross- 
section  of  the  vapour  film,  or  the  mist,  or  both  ;  (2)  by  a  lowering 
of  their  specific  resistances.  To  see  whether  I  could  observe  any 
change  in  the  cross-sections  I  have  traced  a  series  of  enlarged 
images  of  the  arc,  with  four  sets  of  Apostle  carbons,  using 
(1)  solid-solid;  (2)  solid-cored ;  (3)  cored-solid;  (4)  cored-cored 
carbons.  The  positive  carbon  was,  as  usual,  llmm.  and  the 
negative  9mm.  in  diameter,  and  the  arc  was  2mm.  in  length  in 
each  case,  while  the  currents  were  4,  6,  8,  10,  12,  14  amperes. 
The  diagrams  were  traced,  not  only  when  the  arc  was  normal 
in  each  case,  but  also  immediately  after  each  change  of  current, 
so  that  the  effect  on  the  cross-section  of  the  arc  of  both  an 

*  "  The  Eesistance  of  the  Electric  Arc,"  Phil.  Mag.,  1896,  p.  407. 

1 1  call  -—  more  positive  in  one  case  than  in  the  other  when  it  has  either 
oA 

a  larger  positive,  or  a  smaller  negative  value  in  the  first  case  than  in  the 
second. 


MEAN  CROSS-SECTION  OF  MIST. 


419 


instantaneous  and  a  normal  change  of  current  might  be  seen. 
Fig.  128  shows  the  first  set  of  diagrams  of  the  normal  arc; 
the  others  are  too  numerous  to  publish,  but  the  mean  cross- 
sections  of  the  purple  part — the  mist — in  each,  measured  as  in 
Fig.  128,  may  be  found  in  Table  LV.,  those  marked  "non- 
normal  "  belonging  to  the  arc  immediately  after  the  change  of 
current,  and  those  marked  "  normal  "  to  the  arc  after  all  the 
conditions  had  become  steady  again. 

Table  LV. — Mean  Cross-Section  of  Mist  betiveen  Solid- Solid, 
Solid-Cored,  Cored-Solid  and  Cored-Cored  Apostle  Carbons, 
llmm.  and  9mm. 

Length  of  Arc,  2mm. 


Current  in 
Amperes. 

Normal. 

Non-  Normal. 

S.S. 

S.C. 

C.S. 

C.C. 

S.S. 

S.C. 

C.S. 

C.C. 

4 
6 
8 
10 
12 
14 

4-8 
9-8 
16-2 
23-4 
34-9 
41-2 

6-95 
8-3 
14-2 
20-75 
27-6 
35-0 

4-0 
6-05 
11-0 
13-55 
17-7 
24-5 

3-3 
5-6 
8-9 
11-9 
16-55 
20-0 

9-5 
17-6 
21-5 
34-1 

8-4 
11-1 
19-0 
26-9 
39-4 

6-25 
12-0 
18-7 
20-1 

3-5 
5-8 
111 
16-7 
18-7 

With  a  single  exception,  every  number  in  each  set  is  smaller 
than  the  corresponding  number  in  the  preceding  column. 
Hence,  with  all  these  arcs  the  mean  cross-section  of  the  mist, 
for  a  given  current,  was  largest  when  both  carbons  were  solid, 
smallest  when  both  were  cored,  and  was  more  diminished  by 
coring  the  positive  than  by  coring  the  negative.  Fig.  133, 
which  connects  the  mean  cross -section  of  the  mist  with  the 
current  for  each  pair  of  carbons,  besides  showing  well  this 
marked  difference  in  the  influence  of  the  cores,  makes  it 
apparent  that  the  difference  increases,  in  every  case,  with  the 
current. 

We  cannot  measure  the  cross-section  of  the  vapour  film 
directly,  but,  for  a  constant  length  of  arc  it  must  be  roughly 
proportional  to  the  cross-section  of  the  mist  where  it  touches 
the  crater.  These  cross-sections,  which  are  given  in  Table  LVL, 
do  not,  naturally,  vary  nearly  so  regularly  as  the  mean  cross- 
sections,  but  still  we  can  judge  pretty  well  what  are  the  effects 
of  the  various  cores,  Coring  the  positive  carbon,  for  instance, 

EB2 


420 


THE  ELECTRIC  ARC. 


distinctly  diminishes  the  cross-section  of  the  vapour  film;  for 
all  but  one  number  in  column  (3)  is  less  than  the  correspond- 
ing one  in  column  (1),  and  every  number  in  column  (7)  is  less 
than  the  corresponding  one  in  column  (5).  Coring  the  negative 
carbon,  on  the  other  hand,  only  seems  to  diminish  the  cross- 
section  which  the  vapour  film  assumes  immediately  after  a 


30 


K) 


0  4  6  8  10  12  14 

Current  in  Ampere,?. 

FIG.  133. — Curves  connecting  the  Mean  Cross -Section  of  the  Arc  Mist 
with  the  Current  for  Solid-Solid,  Solid-Cored,   Cored-Solid,  and  Cored- 
Cored  Carbons,  llmm.  and  9mm.  in  diameter. 
Length  of  Arc,  2mm. 

change  of  current,  for  while,  in  the  non-normal  section,  each 
number  in  (6)  is  less  than  in  (5),  and  in  (8)  two  are  Jess  than 


EFFECT  OF  CORES  ON  CROSS-SECTION  OF  ARC.    421 


in  (7),  one  is  equal,  and  only  one  is  greater,  in  the  normal 
section  the  numbers  in  (2)  are  sometimes  less  and  sometimes 
greater  than  in  (1),  and  those  in  (4)  are  nearly  all  greater  than 
those  in  (3). 

Thus,  taking  Tables  LV.  and  LVI.  together,  we  find  that  a 
core  in  the  positive  carbon  keeps  both  the  mist  and  the  vapour 
film  from  being  as  large  as  they  would  be  with  a  solid  positive, 
both  immediately  after  a  change  of  current  and  when  the  arc 
is  normal  again.  Coring  the  negative,  on  the  other  hand,  while 
it  has  the  same  effect  on  the  cross-section  of  the  mist  as  coring 

Table  LVI. — Cross-Section  of  Mist  where  it  touches  Crater, 
Solid- Solid,  Solid-Cored,  Cored- Solid,  Cored-Cored  Apostle 
Carbons,  llmm.  and  9mm. 

Length  of  Arc,  2mm. 


Current  in 

Normal. 

Non-Normal. 

Amperes. 

S.S. 

S.C. 

C.S. 

C.C. 

S.S. 

S.C. 

C.S.      C.C. 

4 

(1) 
2-9 

(2) 
7-8 

(3) 
3-2 

(4) 
2-9 

(5) 

(6) 

(7)     !     (8) 


6 

6-8 

9-0 

5-3 

5-8 

10-9 

6-25 

6-25  !    3-6 

3 

16-0 

13-0 

10-9 

14-4 

16-0 

9-0 

10-9        6-25 

10 

23-0 

26-0 

12-25 

21-2 

19-4 

16-8 

15-2      15-2 

12 

32-5 

25-0 

17-6 

221 

31-4 

23-0 

17-6      21-2 

14 

39-1      36-0 

23-0 

24-0 

33-6 

...       19-4 

the  positive,  only  diminishes  the  cross-section  of  the  vapour  film 
immediately  after  a  change  of  current.  If,  therefore,  coring 
either  carbon  produced  nothing  but  an  alteration  in  the  cross- 
section  of  the  arc,  the  resistance  of  the  arc,  and,  consequently, 
the  P.D.  between  the  carbons  would  be  increased  by  the  coring. 
It  follows,  therefore,  that  the  diminution  of  the  P.D.  between 
the  carbons  actually  observed  with  cored  carbons  must  be 
caused  by  a  lowering  of  the  specific  resistance  of  the  vapour 
film  or  the  mist,  or  both  ;  and  this  lowering  must  be  so  great 
that  it  must  more  than  compensate  for  the  diminution  in  their 
cross-sections. 

It  is  easy  to  see  how  the  vapour  and  mist  from  a  core  in  the 
positive  carbon  must  alter  the  specific  resistance  of  the  arc, 
but,  since  the  negative  carbon  does  not  volatilise,  there  seems 
to  be  no  reason  why  coring  it  should  have  the  same  effect. 


422  THE  ELECTRIC  ARC. 

The  core,  however,  consists  of  a  mixture  of  carbon  and  metallic 
salts;  and  metallic  salts  have  a  lower  temperature  of  volatilisa- 
tion than  carbon,  so  that  these  salts  may  easily  be  volatilised  by 
the  mist  touching  them,  and,  mingling  with  it,  lower  its  specific 
resistance. 

Now  take  the  fact  that  with  a  constant  length  of  arc  and 
increasing  current  the  P.D.  always  diminishes  less  if  the  positive 
carbon  is  cored  than  if  it  is  solid,  and  that  the  reduction  of 
diminution  is  sometimes  so  great  that  the  P.D.  remains  constant 
for  a  large  increase  of  current,  and  sometimes  even  increases 
some  what,  instead  of  steadily  diminishing,  as  it  does  when  both 
carbons  are  solid. 

In  Chapter  IV.  (p.  133)  this  point  was  dealt  with  on  the 
assumption  that  "  with  a  given  negative  carbon  the  P.D. 
required  to  send  a  given  current  through  a  fixed  length  of  arc 
depends  principally,  if  not  entirely,  on  the  nature  of  the 
surface  of  the  crater,  being  greater  or  less,  according  as  the 
carbon  of  which  that  surface  is  composed  is  harder  or  softer." 
This  can  now  be  modified  into  the  following,  which  is  no 
longer  a  pure  assumption,  but  must  rank  as  a  proposition : — 
"With  a  given  negative  carbon,  current,  and  length  of  arc, 
the  P.D.  between  the  carbons  depends  principally,  if  not 
entirely,  on  the  nature  of  the  carbon  that  forms  the  surface  of 
volatilisation,  being  higher  or  lower,  according  as  that  carbon 
is  more  or  less  free  from  metallic  salts." 

The  explanation  given  in  Chapter  IV.  can  now  be  extended 
in  the  following  manner  : — 

Every  increase  of  current  entails  an  enlargement  of  the 
cross-section  of  the  arc,  and  a  consequent  tendency  of  the  P.D. 
to  diminish.  While  the  current  is  so  small  that  the  volatilising 
surface  does  not  completely  cover  the  core,  the  increase  of 
cross-section  is  unaccompanied  by  any  change  in  the  specific 
resistance  of  the  arc.  When  the  current  is  so  large,  however, 
that  the  solid  carbon  round  the  core  begins  to  volatilise, 
since  the  resulting  vapour  and  mist  have  higher  specific 
resistances  than  those  of  the  core,  each  increase  of  current 
is  accompanied  by  two  tendencies  in  the  P.D. — the  one 
to  fall,  on  account  of  the  larger  cross-section,  the  other 
to  rise,  because  of  the  higher  specific  resistance  of  the 
vapour  and  mist.  The  curve  connecting  the  P.D.  with  the 


EFFECT  OF  GORES  ON  P.D.  BETWEEN  CARBONS.  423 


current  must,  therefore,  be  compounded  of  two.  One,  such 
as  ABC  (Fig.  134),  which  would  connect  the  P.D.  with 
the  current  if  the  positive  carbon  were  composed  entirely  of 


\ 


Current 


Current 

Fia.  134. — Curves  exemplifying  the  Changes  in  the  Curve  connecting  P.D. 
with  Current  caused  by  a  Core  in  the  Positive  Carbon. 

core,  and  the  other,  DEF,  connecting  the  rise  of  P.D.,  due  to 
the  increase  of  specific    resistance,    with   the   current.     The 


424  THE  ELECTEIC  AUG. 

curve  connecting  the  true  P.D.  with  the  current  is  found  by 
adding  each  ordinate  of  DEF  to  the  corresponding  ordinate  of 
ABC  as  indicated  in  the  dotted  line.  Whether  this  resulting 
curve  has  the  form  GHK,  or  MNP,  or  QRS  (Fig.  134),  depends 
evidently  upon  the  relation  between  the  increase  of  the  cross- 
section  and  the  rise  of  specific  resistance,  i.e.,  on  the  rela- 
tive structures  and  cross-sections  of  the  core  and  the  outer 
carbon. 

The  fact,  already  obtained  from  Table  LV.,  that,  for  the 
same  current  and  length  of  arc,  the  vapour  film,  and  conse- 
quently the  crater,  is  smaller  with  a  cored  than  with  a  solid 
positive  carbon  explains  why  the  arc  can  carry  such  a  much 
larger  current  without  hissing  when  the  positive  carbon  is 
cored.  For,  since  hissing  is  the  result  of  that  direct  contact 
of  the  crater  with  the  air  that  follows  when  it  grows  too  large 
to  cover  the  end  only  of  the  positive  carbon,  and  since  this 
must  happen  with  a  smaller  current  the  larger  the  crater  is 
with  a  given  current,  it  must  happen  with  a  smaller  current 
when  the  positive  carbon  is  solid  than  when  it  is  cored. 

OTT 

The  Influence  of  the  Core  on  the  Value  of  -5— . 

oA 

We  have  next  to  consider  the  influence  of  the  cores  on  the 

OTT 

value  of  — ,  when  such  an  alternating  current  is  superimposed 
oA. 

on  a  direct-current  normal  arc  that  the  resistance  of  the  arc  is 
affected  by  the  superposition.  Here  we  have  to  deal,  not  with 
the  whole  P.D.  between  the  carbons,  but  with  the  change  in 
that  P.D.  that  accompanies  a  given  change  of  current,  and  I 
shall  show  that  the  effect  of  the  core  on  this  change  is  always 

oy 

to  add  a  positive  increment  to  — ,  the  amount  of  which  depends 

oA 

on  the  current,  the  length  of  the  arc,  and  the  frequency  of  the 
alternating  current. 

CNTT 

The  influence  of  the  core  on  the  value  of  ~  is  two-fold  :  it 

oA 

alters  the  amount  by  which  the  cross-sections  of  the  vapour 
film  and  the  mist  change,  with  a  given  change  of  current ;  and 
it  makes  their  specific  resistances  vary  with  the  current.  We 
will  take  each  separately — the  change  of  cross-section  first. 

OTT 

I  shall  call  the  part  of  ,     that  depends  on  the  change  of  cross- 


DEFINITIONS  OF         AND  425 

0A  cA 

sv 

section  -«-/,  and  the  part  that  depends  on  the  variation  in  the 

.  6V 

specific  resistance  K— ,  so  that 

5A 

SV  =  SV,     8V. 
8A     SA      SA" 

#OM;  the  Change  in  the  Cross- Sections  of  the  Mist  and  the  Vapour 
Film  due  to  a  Change  of  Current  is  affected  by  Coring  either 
or  both  Carbons. 

I  have  already  pointed  out  (p.  402)  that  if,  when  the  current 
is  increased,  the  ratios  of  the  new  cross-sections  of  the  mist  and 
the  vapour  film  to  the  old  are  greater  than  the  ratio  of  the 
new  current  to  the  old,  then  the  resistance  of  the  arc  must 
have  been  diminished  more  than  the  current  was  increased,  and 

SV 

—  must  be  negative  (provided  always  that  the  specific  resis- 

oA 

tance  of  the  arc  has  not  been  altered).     Similarly,  when  the 
ratios  of  the  cross- sections  are  smaller  than  that  of  the  current 

—  must  be  positive. 

In  order  to  see  the  effect  of  the  cores  on  these  ratios  in  the 
experiments  of  which  the  results  are  given  in  Tables  LV. 
and  LVI.,  Tables  LVII.  and  LVIII.  have  been  drawn  up,  in 
which  the  cross-section  ratios  are  found  by  dividing  the 
cross-section  for  each  current  by  the  cross-section  for  the 
next  smaller  current ;  and  the  current  ratios  by  dividing  each 
current  by  the  next  smaller  current.  For  the  non-normal 
ratios  the  larger  cross-sections  were  taken  from  the  non-normal 
sets  in  Tables  II.  and  III.  and  the  smaller  from  the  normal^ 
because  it  is  the  effect  of  the  core  when  the  alternating  current 
is  superimposed  on  a  normal  arc  that  we  are  considering,  and 
because  also  the  non-normal  numbers  in  these  tables  were  found 
by  suddenly  increasing  the  current  when  the  arc  was  normal. 
For  the  normal  ratios  both  numbers  were  taken  from  the 
normal  sets  in  Tables  LV.  and  LVI.  For  instance,  the  normal 
cross-section  for  a  current  of  8  amperes  with  the  +  solid  —  cored 
carbons  in  Table  LV.  is  14*2,  and  the  non-normal  cross- 
section  for  10  amperes  is  19-0,  while  the  normal  cross-section 
for  the  same  current  is  20*75.  Thus,  when  the  current 

is  increased  from  8  to  10  amperes,  the  current  ratio  is  —  =  1-25 

o 


426 


THE  ELECTRIC  ARC. 


the    non-normal    cross-section   ratio    with    these    carbons    is 

1Q  90*75 

_  =  1-34,  and  the  normal  is  "    '|  =  1-46.  In  this  case,  there- 
fore, —  would  be  negative,  as  far  as  the  change  in  the  cross- 

SA 

section  of  the  mist  was  concerned,  both  when  the  change  was 

Table  LVII. — Ratio  of  Mean  Cross- Section  of  Mist    to   Cross- 
Section  with  Next  Smaller  Current  taken  from  Table  LV. 

Length  of  Arc,  2mm,. 


Change  of 
Current. 

Current 
Ratios. 

Ratios  of  Mean  Cross  Sections. 

Normal. 

Non-Normal. 

S.S. 

S.C. 

C.S. 

C.C. 

S.S. 

S.C. 

C.S. 

C.C. 

(1) 

4  to  6 
6to  8 
8  to  10 
10  to  12 
12tol4 

(2) 
1-5 
1-33 
1-25 
1-20 
117 

(3) 
204 
1-65 
1-44 
1-49 
118 

(4) 
1-2 
1-71 
1-46 
1-33 
1-25 

(5) 
1-51 
1-82 
1-23 
1-31 
1-38 

(6) 
1-7 
1-6 
1-33 
1-39 
1-21 

(7) 
1-98 
1-8 
1-33 
1-46 

(8) 
1-21 
1-33 
1-34 
1-30 
1-43 

(9) 
1-56 
1-98 
1-70 
1-48 

(10) 
1-06 
1-04 
1-25 
1-40 
113 

Table  LVIII. — Ratios  of  Cross- Sections  of  Mitt  where  it  touches 
the  Crater,  taken  from  Table  LV. 

Length  of  Arc,  2mm. 


Change  of 
Current. 

Current 
Ratios. 

Ratios  of  Cross-  Sections  at  Crater. 

Normal. 

Non  -Normal. 

S.S. 

S.C. 

C.S. 

C.C. 

S.S. 

S.C. 

C.S.      C.C. 

(1) 

4to  6 
6to  8 
8  to  10 
10tol2 
12  to  14 

(2) 
1-5 
1-33 
1-25 
1-20 
117 

(3) 
2-34 
2-35 
1-44 
1-41 
1-20 

(4) 
1-07 
1-44 
2-00 
0-96 
1-44 

(5) 
1-66 
2-05 
112 
1-44 
1-31 

(6) 
2-0 
2-5 
1-47 
1-04 
1-09 

(7) 
3-76 
2-35 
1-21 
1-37 

(8) 
0-8 
1-00 
1-29 
0-88 
1-34 

(9) 
1-95 
2-06 
1-40 
1-44 

(10) 
1-24 
1-08 
1-05 
1-00 
0-88 

non-normal  and  when  it  was  normal,  for  both  1-34  and  1-46 
are  greater  than  1'25,  the  current  ratio.  The  non-normal 
ratios  show  the  effect  of  the  core  on  the  change  in  the 

OTT 

resistance  of  the  arc,  and  therefore  on  — ,  when  the  frequency 

oA. 

of  the  alternations  is  so  great  that  the  carbons  do  not  change 


EFFECT  OF  CORES  ON  VARIATION  OF  CROSS-SECTION.  427 

their  shapes ;  and  the  normal,  when  it  is  so  small  that  the  are 
remains  normal  throughout. 

Of  course,  to  imitate  the  effect  of  an  alternating  current 
completely  it  would  be  necessary  to  diminish  the  current 
suddenly  as  well  as  suddenly  increasing  it,  but  as  this  would  only 
alter  the  signs  of  both  8V  and  8A,  without  materially  changing 
their  relative  values,  it  is  not  necessary  for  our  purpose. 

The  most   important    point   to  observe  in   these   tables  is 

8V 
whether  — -  is  negative  or  positive  with  each  set  of  carbons. 

i.e.,  whether  the  cross-section  ratios  are  greater  or  less  than 

the  current  ratios.     Take,  first,  the  non-normal  ratios.     When 

K\T 
the  positive  carbon  alone  is  cored  — - -    is   decidedly   negative, 

oA 

for  all  the  cross-section  ratios  in  column  (9)  of  both  tables 
are  greater  than  the  corresponding  current  ratios  in  column 
(2).  Moreover,  with  this  particular  length  of  arc  and  these 

8V 
currents  the  non-normal  -  - -c  appears  to  be  unaffected  by  coring 

oA 

the  positive  carbon  alone,  for  the  non-normal  cross-section 
ratios  in  column  (9)  of  each  Table  are  in  some  cases  greater 
and  in  others  less  than  those  in  column  (7).  When  the  negative 

8V 
carbon  alone  is  cored,  the  non-normal  value  of  .— ~  appears   to 

oA 

be  negative,  but  approaching  the  zero  point;  for  in  Table 
LVII.  one  cross-section  ratio  in  column  (8)  is  less  than 
the  corresponding  current  ratio,  one  is  equal  and  three  are 
greater,  while  in  Table  LVIII.  three  are  less  and  two  are 
greater.  When  both  carbons  are  cored,  the  non-normal  value 

8V 
of  — • c  is  positive ;  for  three  out  of  the  five  of  the  numbers  in 

oA 

column  10  of  Table  LVL,  and  the  whole  of  those  in  the  same 
column  of  Table  LVII.,  are  less  than  the  corresponding 
numbers  in  column  (2). 

Turning  next  to  the  normal  ratios,  we  find  that  when  the 

8V 

positive  carbon  alone  is  cored   — -  has  still  much  the  same 

oA 

negative  value  as  when  both  carbons  are  solid,  since  th« 
numbers  in  column  (5)  differ  very  little  on  the  whole  from 
those  in  column  (3).  When,  on  the  other  hand,  it  is  the 
negative  carbon  alone  that  is  cored  there  is  a  change,  for 


428  THE  ELECTtilC  ARC. 

8V 

instead  of  being  a  little  below  zero  — -  is  decidedly  negative, 

oA 

since  in  Table  LVII.  all  but  one  of  the  numbers  in  column  (4), 
and  in  Table  LVIII.  all  but  two  are  greater  than  the  corre- 
sponding numbers  in  column  (2).  When  both  carbons  are 
cored  there  is  an  even  greater  difference  between  the  normal 

<JTT 

and  non-normal  values  of  — c.     For,  in  Table  LVII.  all  the 

oA 

numbers  in  column  (6),  and  in  Table  LVIII.  all  but  two  are 
greater  than  the  corresponding  current  ratios,  showing  that 

— c  is  negative  for  normal  changes  of  current,  though  it  is 

oA 

positive  for  non-normal  changes,  with  these  carbons,  currents, 

and  lengths  of  arc.     Thus,  coring  the  negative  carbon  retards 

the  change  of  cross-section  that  follows  a  change  of  current, 

for  while  this  change  follows  immediately  after  the  change  of 

current  when  the  negative  carbon  is  solid,  when  it  is  cored  an 

appreciable  time  elapses  before  it  takes  place. 

K\T 
To  sum  up  the  changes  in  the  value  of  — -^  produced  by 

oA 

coring  one  or  both  of  the  carbons,  we  find  that  while  coring 
the  positive  carbon  alone  makes  very  little  difference  in  either 
the  normal  or  the  non-normal  change  of  cross- section  that 
accompanies  a  given  change  of  current,  coring  the  negative 
carbon  diminishes  the  change  of  cross-section  both  for  normal 
and  non-normal  changes  of  current,  but  more  for  the  second 
than  for  the  first,  and  more  when  both  carbons  are  cored  than 
when  the  negative  alone  is  cored.  Thus  coring  the  negative 
carbon  both  diminishes  and  retards  the  change  in  the  cross- 
sections  of  the  arc  that  accompany  a  change  of  current,  since 
the  change  of  cross-section  is  less  immediately  after  the  current 
is  changed  than  it  is  later,  after  the  arc  has  become  normal 
for  the  new  current.  This  retardation  of  the  change  of  cross- 
section  is  quite  sufficient  to  account  for  the  fact  already 
mentioned  on  p.  406,  viz.,  that  if  I  quickly  altered  the  resis- 
tance in  the  circuit  outside  the  arc,  when  both  carbons  were 
cored,  I  could  sometimes  see  the  first  quick  swing  of  the  volt- 
meter needle  in  the  same  direction  as  that  of  the  ammeter, 
but  never  when  both  were  solid.  For,  as  the  resistance  did 
not  alter  directly  after  the  current  with  the  cored  carbons,  the 
new  current  would  be  flowing  through  the  old  resistance  for  an 


CHANGE  OF  SPECIFIC  RESISTANCE  DUE  TO  CORE.    429 

appreciable  time  after  the  change,  and  so  the  accompanying 
change  of  P.D.  in  the  same  direction  as  the  change  of  current 
would  be  able  to  influence  the  voltmeter  needle. 

The  Change  in  the  Specific  Resistance  of  the  Arc  produced  by  a 
Change  of  Current  when  Either  or  Both  Carbons  are  Cored. 

8V  SV 

We  have  next  to  consider  — J,  the  part  of  —  that  depends 

O  zx  OiY. 

on  the  changes  in  the  specific  resistances  of  the  mist  and 
vapour  that  occur  with  each  change  of  current  when  either  or 
both  carbons  are  cored. 

Coring  the  negative  carbon  must  have  a  very  different  effect 
from  coring  the  positive,  for  whereas,  in  the  first  case  the 
whole  of  the  vapour  and  almost  the  whole  of  the  mist  issues 
-from  the  uncored  carbon,  the  core  only  contributing  a  little 
metallic  vapour  to  the  mist  in  contact  with  it,  in  the  second 
the  whole  comes  from  the  cored  carbon.  Thus,  while  with  the 
cored  negative  the  vapour  is  always  solid-carbon  vapour,  and 
the  mist  is  practically  solid-carbon  mist,  even  with  the  smallest 
currents,  with  the  cored  positive  the  vapour  and  mist  are  both 
core  vapour  and  mist  alone  until  the  current  is  large  enough 
for  the  volatilising  surface  to  cover  the  whole  core,  and  only 
begins  to  have  an  admixture  of  solid-carbon  vapour  and  mist 
when  the  current  is  larger  than  this.  When,  therefore,  the 
negative  carbon  alone  is  cored,  the  specific  resistance  of  the 
vapour  is  constant,  and  that  of  the  mist  increases  with  each 
small  increase  of  current,  but  more  and  more  slowly,  with  the 
same  addition  of  current,  the  larger  the  original  current  before 

«TT 

the   addition   is   made.     The  curve  connecting  . — -  with  the 

oA. 

normal  current  in  this  case  must,  therefore,  be  of  the  form  ABC 
(Fig.  135),  for  the  specific  resistance  must  change  most  when  the 
current  is  just  large  enough  for  the  mist  to  cover  the  whole 
core,  and  the  amount  by  which  it  changes  must  steadily 
diminish  as  the  direct  current  increases  after  that,  till  it 
becomes  practically  zero  with  very  large  currents,  so  that  the 
curve  becomes  asymptotic  to  the  axis  of  current. 

When  the  positive  carbon  alone  is  cored,  the  curve  is  quite 
different.  If  the  arc  always  remained  perfectly  central,  it 
would  be  of  the  form  DEFG  (Fig,  135).  The  specific  resistances 


430 


THE  ELECTRIC  ARC. 


of  the  vapour  and  mist  would  remain  constant  till  the 
volatilising  surface  was  large  enough  to  cover  the  core,  so  that, 

until  then,  — ^  would  be   zero   and  DE   would   be  the   first 

SA 

part  of  the  curve.  The  first  increment  of  current  that  was 
added  after  this  would  increase  the  specific  resistances  more 
than  any  subsequent  increment,  because  this  would  be  the  point 
at  which  the  specific  resistances  of  the  existing  vapour  and  mist 
and  of  those  added  would  be  most  different.  Therefore,  the 
curve  would  rise  suddenly  at  E.  After  this,  each  addition 
to  the  normal  current  would  make  the  change  of  specific 
resistance  due  to  the  added  small  non-normal  increment  of 
current  smaller  and  smaller,  so  that  the  curve  would  fall 
towards  the  axis  of  current  as  shown  in  FG.  Finally,  there 


Current  in  Amperes. 

Fio.  135.-—  Curves  'connecting  — t-  with  Current  for  Constant  Length  of  Arc. 
5A 

would  already  be  so  much  solid-carbon  vapour  and  mist  in 
the  arc  that  the  addition  of  a  little  more  would  make 
practically  no  change,  so  that  this  curve  also  is  asymptotic  to 
the  axis  of  current.  The  fact  that  the  arc  is  never  really  quite 
central,  and  that  the  volatilising  surface  must  therefore  cover 
a  little  solid  carbon  long  before  it  is  larger  than  the  core,  must 
introduce  some  modifications  into  the  first  part  of  the  curve, 
shortening  DE  and  making  EF  rise  less  abruptly,  something 
like  DF'G ;  but  these  modifications  are  unimportant. 

When  both  carbons  are  cored  the  curve  must  be  like  DEHK, 
or  rather  DH'K,  because  the  effect  of  the  metallic  vapour 
from  the  negative  core  will  be  added  to  that  of  the  positive 
core,  and  the  change  of  specific  resistance,  when  solid -carbon 
mist  begins  to  be  added  will,  therefore,  be  greater. 


EFFECT  OF  CORES  ON  VALUE  OF  431 

cA 

8V 

IToir  the  whole  Value  of  —   is  affected   by  Coring   either  nr  both 
oA 

Carbons. 

By  combining  the  two  changes  in  the  resistance  of  the  arc 
introduced  by  the  core — viz.,  that  due  to  the  difference  of  the 
changes  in  the  cross-sections  of  the  arc  and  that  produced  by 
the  alterations  in  its  specific  resistance — we  can  see  how  the 

CVTT 

complete  value  of  ^-  is  affected  by  the  core. 

oA 

From  what  has  been  said  on  p.  427  it  is  clear  that,  if  the  cross- 
section  ratios  in  Tables  LVIL  and  LVIII.  can  be  considered 

f\\T 

typical,  —j-2  never  has  a  greater  negative  value  when  the  positive 

carbon  alone  is  cored  than  when  both  are  solid  ;  never  a  greater 
negative  value  when  the  negative  alone  than  when  the  positive 
alone  is  cored,  and  never  a  greater  negative  value  when  both 

8V 

are  cored  than  when  the  negative  alone  is  cored.     But  —  is 

oA 

zero  when  both  carbons  are  solid,  is  greatest  when  both  are 
cored,  and  has  always  some  positive  value,  however  small, 
when  either  carbon  alone  is  cored.  Consequently,  when  the 
superimposed  alternating  current  alters  the  resistance  of  the 

8V 
arc,  if  all  other  things  are  equal,  —  is  more  positive  when 

oA 

either  carbon  is  cored  than  when  both  are  solid,  and  most 
positive  when  both  are  cored. 

8V 
The  general  effect  on  ^—  of  coring  either  or  both  carbons  is 

oA 

given  in  the  preceding  paragraph,  but  with  a  given  root  mean 

SV 

square  value  of  the  alternating  current  ^  depends,  not  only  on 

oA 

the  nature  of  the  carbons,  but  also  on  the  magnitude  of  the 
direct  current,  the  length  of  the  arc,  and  the  frequency  of 
the  alternating  current.  To  complete  our  knowledge  of  the 

8V 
influence  of   cores  on  the   value  of  ^,  therefore,   we   must 

examine  the  effect  they  produce  on  the  curves  connecting  each 

OT7" 

of  these  variables  with  — .  when  the  others  are  constant.    Take, 

8V 
first,  the  curves  connecting  -^  with  the  magnitude  of  the  direct 

oA. 

current, 


432 


THE  ELECTRIC  ARC. 


The   Effect  produced  b\j  Coring  either  or  both  Carbons  on  the 

Curve  connecting  the  Non-Normal  Value  of  —  with  A,  when 

oA. 
the  Length  of  the  Arc  is  Constant. 

In  Tables  LVII.  and  LVIII.  the  cross-section  ratios  for  solid 
carbons  differ  less,  on  the  whole,  from  the  corresponding  current 
ratios  the  larger  the  current  on  which  the  increase  of  2  amperes 


£13 


Zero  Line 


Current  in  Amperes. 

FIG.  136.— Curves  connecting       c  with  the  Current  for  a  Constant  Length 
of  Arc.  5A 

ABC— Solid-Solid  or  Cored-Solid  Carbons  ;  DBF -Solid-Cored  ; 
GHK— Cored-Cored. 

has  been  superimposed.     This  shows  that  with  solid  carbons, 

6V 
when  the  length  of  the  arc  is  constant,  — -  diminishes  as  the 

oA 

current  increases.     Consequently,  the  curve  for  solid  carbons 
is  of  the  form  ABC  (Fig.  136).    With  cored  carbons  the  curves. 


CONNECTION  VET  WEEN      -  AND  DIRECT  CURRENT.  433 

oA 

r?V 

depend  not  only  on  — -,  which  is  obtained  from  Tables  LVII. 

oA 

$y 

and  LVIIL,  but  also  on  Jj2,  the  curves  connecting  which  with 

6A-  SV 

A  are  given  in  Fig.  135.     The  curves  connecting  — -c  with  A 

oA. 

cannot  be  obtained  straight  from  Tables  LVII.  and  LVIIL, 
because  the  values  are  too  irregular,  but  we  can  deduce  them 
from  what  we  already  know.  For  instance,  when  the  positive 
carbon  alone  is  cored  it  must  have  the  same  form,  ABC,  as 
when  both  are  solid,  since  the  change  of  cross-section  due  to  a 
given  change  of  current  is  not  materially  altered  by  coring  the 
positive  carbon  alone.  Coring  the  negative  carbon  alone 

8V 
diminishes  the  negative  value  of  — -,  and  must  diminish  it 

oA. 

most  when  the  current  is  least,  for  it  is  then  that  the  metallic 
vapour  from  the  core  will  be  expended  on  the  smallest  quantity 
of  hard  carbon  mist,  and  will,  consequently,  have  most  effect. 
Hence  the  curve  for  a  cored  negative  and  solid  positive  carbon 

SVC 
must  resemble  DEF  (Fig.  136),  and  the  current  for  which  ~- 

oA. 

becomes  positive,  if  any,  will  depend  upon  the  length  of  the 
arc  and  the  frequency.  Finally,  it  has  been  shown  that  with 

<>TT 

both  carbons  cored  — — £  is  even  more  positive  than  when  the 

oA. 

negative  only  is  cored  (p.  431),  so  that  the  curve  with  both 
carbons  cored  must  resemble  GHK  (Fig.  136),  since  the  same 
reasoning  as  before  shows  that  the  cores  must  have  least  effect 

OTT  C>TT 

on  both  — ~  and  — -  when  the  current  is  largest. 

oA  oA 

OT7" 

To  find  the  full  curves  connecting  —  with  A  for  each  pair  of 

oA. 

carbons,  we  have  only  to  add  each  ordinate  of  each  curve  in 
Fig.  135  to  the  corresponding  ordinate  of  the  curve  for  the  same 
carbons  in  Fig.  136.  Curves  resembling  those  that  would  be 
thus  obtained  for  one  length  of  arc  and  frequency  of  alternating 
current  are  given  in  Fig.  137.  The  exact  distance  of  each  above 
or  below  the  zero  line  and  the  exact  points  where  it  cuts  that 
line  must,  of  course,  depend  upon  the  length  of  arc  and  fre- 
quency of  alternating  current  for  which  the  curves  are  drawn, 
but  their  relative  shapes  and  positions  must  be  similar  to  those 
in  Fig.  137  whatever  the  length  of  the  arc  and  the  frequency. 

PP 


434 


THE  ELECTRIC  ARC. 


OTT 

Next  take  the  curve  connecting  ^  with  I,  the  length  of 

oA 

the  arc,  when  the  frequency  of  the  alternating  current  and  the 
value  of  the  direct  current  are  both  constant. 


fv] 


Zero  Line 


Current  in  Amperes. 
FIG.  137.— Curves  connecting—-  with  A  for  a  Constant  Length  of  Arc 

when  the  Superimposed  Alternating  Current  Affects  the  Resistance  of 
the  Arc. 

ABC— Solid-Solid  Carbons  ;  AGHK— Cored-Solid  ; 
DEF— Solid-Cored  ;  DMN— Cored- Cored. 

The  Effect  produced  by  Coring  either  or  both  Carbons  on   the 

£T7" 

Curve  connecting   the   Non-Normal   Value  of   —  with  the 
Length  of  the  Arc,  when  A  is  Constant. 

Messrs.  Frith  and  Rodgers  found  that,  with  a  constant  current 
of  10  amperes,  curves  somewhat  resembling  those  in  Fig.  139 


CONNECTION  BETWEEN       A  NI)  LENGTH  OF  ARC.    435 

oA 

OTT 

connected  —  with  the  length  of  the  arc  with  Apostle  carbons 
oA 

of  llmm.  and  9mm.  In  order  to  see  why  the  curves  should 
take  this  peculiar  form  we  must  start,  first  of  all,  with  the 
lowest,  for  which  both  carbons  were  solid, 

PQ  (Fig.  138)  is  the  rise  of  P.D.  that  would  accompany  the 
increase  of  current  SA  with  an  arc  of  I  millimetres  if  the 
resistance  of  the  arc  did  not  alter  with  the  current.  QR  is 
the  fall  of  P.D.  due  to  the  enlargement  of  the  vapour  film  and 
the  mist.  When  the  current  increases  from  A  to  A  +  SA, 
therefore,  the  P.D.  actually  falls  from  P  to  E.  Now,  the  rise 
PQ  depends  only  on  the  amount  by  which  the  current  is 
increased,  and  the  resistance  through  which  that  increased 
current  has  to  flow,  i.e.,  on  SA,  A,  and  I;  or,  since  A  and  SA 
are  supposed  to  be  the  same  for  each  length  of  arc,  PQ  depends 
simply  on  I,  and  increases  directly  as  I  increases. 


Time 


FIG.  138.— Time-Change  of  P.D.  due  to  a  Change  of  Current. 

The  fall  of  P.D. — QR — is  more  complex.  It  depends  prin- 
cipally on  how  much  of  the  extra  carbon  volatilised  by  the 
larger  current  remains  between  the  carbons,  and  how  much 
escapes  along  them.  When  the  carbons  are  blunt  more  will 
remain  than  when  they  are  pointed,  and  as  the  carbons  get 
blunter,  with  the  same  current,  as  the  arc  is  lengthened, 
so  the  resistance  must  diminish  more,  on  account  of  the 
increase  of  the  current,  the  longer  the  arc.  But  the  blunting 
of  the  carbons,  which  is  a  rapid  affair  when  the  arc  is  short, 
takes  place  more  and  more  slowly  as  it  is  lengthened,  till  at 
last  the  addition  of  a  millimetre  or  so  makes  practically  no 

FP2 


436 


THE  ELECTRIC  ARC. 


difference.  Hence,  the  diminution  of  resistance  due  to  the 
addition  of  SA  to  the  current  increases  rapidly  at  first,  when 
the  arc  is  short,  and  more  and  more  slowly  as  the  arc  lengthens, 
till  it  becomes  practically  constant;  and  hence,  also,  QR — the 
fall  of  P.D.  accompanying  this  diminution — increases  more  and 


\ 


Zero  Line 


Length  of  Arc. 

FIG.  139.— Curves  connecting  ^  with  the  Length  of  the  Arc  for  a  Constant 

Current  when  the  Superimposed  Alternating  Current   Affects   the 
Resistance  of  the  Arc. 

ABC-Solid-Solid  Carbons  ;   DBF  and  GHK— One  Carbon  Solid,  One 
Cored  ;  MNP— Cored-Cored. 

more  slowly  as  the  arc  is  lengthened.     Thus,  while  the  rise 

P.D.—PQ— increases   at   a   constant  rate   as   the    arc   is 

lengthened,   the  fall— QR— increases   at   a   diminishing  rate, 


CONNECTION  BETWEEN         AND  FREQUENCY.    437 

While  the  arc  is  so  short,  therefore,  that  QR  increases  more 
rapidly  than  PQ  when  I  is  increased,  the  whole  fall  of  P.D. 
— PS — will  increase  with  the  length  of  the  arc,  or,  since 

8V 
PS  is  -  8V,  and  8A  is  the  same  for  all  the  lengths  of  arc,  -  — 

increases  as  the  arc  is  lengthened.     When  the  arc  is  so  long 

8V 

that  PQ  increases  faster  than  OR,  -  —  will  diminish  as  the 

oA 

arc  is  lengthened.     Between  the  two  stages  there  must  be  a 

length  of  arc  for  which  -  -=-r  is  a  maximum.     The  curve  con- 

8V 

necting  — -  with  I  for  a  constant  current,  with  solid  carbons, 
oA 

must  therefore  be  of  the  form  ABC  (Fig.  139),  and  there  seems 

8V 

to   be   no   reason   why,    with  very  long  arcs,  —  should  not 

oA 

actually  become  positive,  with  superimposed  alternating 
currents  of  comparatively  low  frequency,  even  with  solid  carbons. 

j>TT 

The  curves  connecting  -—  with  I,  when  cored  carbons  are 

oA 

used  must  resemble  the  curve  for  solid  carbons,  ABC  (Fig.  139), 
but  must  be  higher  up  the  figure  (DEF,  GHK)  when  one 
carbon  is  cored,  and  still  higher  (MNP)  when  both  are  cored. 
Also,  since  a  change  in  the  specific  resistance  of  the  arc  must 

OTT 

have  more  effect  on  the  value  of  ^-r-,  the  longer  the  arc,  the 

oA 

distance  between  the  curves  for  cored  carbons  and  the  curve 
for  solid  carbons  must  increase  as  the  arc  is  lengthened,  as  it 
does  in  Fig.  139. 

The  Effect  produced  by   Coring  either  or  both   Carbons  on   the 

8V 
Curve  connecting  -«-r  with  the  Frequency  of  the  Alternating 

Current. 

ABC  (Fig.  140),  which  is  copied  from  Fig.  132,  is  the  curve 

8V 
for  solid  carbons.     Since  ^  is  always  most  positive  when  both 

carbons  are  cored,  and  more  positive  when  one  is  cored  than  when 
both  are  solid  (p.  431),  the  curve  when  both  carbons  are  cored  must 
resemble  DEF,  and  the  curves  for  one  carbon  cored  and  the 
other  solid  must  lie  between  ABC  and  DEF.  It  follows,  there- 

8V 
fore,  that  the  frequency  with  which  -     becomes  positive,  if  it 


438 


THE  ELECTRIC  ARC. 


is  not  already  positive,  for  normal  changes  of  current  (frequency 
(0  must  be  lower  when  one  carbon  is  cored  than  when  both 
are  solid,  and  lowest  when  both  are  cored.  Thus,  with  the 

same  direct  current  and  length  of  arc  -^—  may  be  positive  for 

oA. 

all  four  sets  of  carbons,  as  at  the  points  C,  P,  K,  F,  or 
positive  for  some  and  negative  for  others,  as  at  B,  N,  H,  E,  or 
negative  for  all.  Moreover,  since  the  true  resistance  of  the 
arc  is  greatest  when  both  carbons  are  solid  and  least  when 


FIG.  140.— Curves  connecting  —  with  the  Frequency  of  the  Super- 
imposed Alternating  Current  for  Solid-Solid,  Solid- Cored,  Cored-Solid 
and  Cored-Cored  Carbons. 


both  are  cored,  and  smaller  when  the  positive  alone  than  when 
the  negative  alone  is  cored,  the  curve  for  two  solid  carbons 
must  cut  all  the  others  at  some  fairly  high  frequencies,  and 
that  for  two  cored  carbons  must  also  cut  the  other  two. 
Hence,  the  curves  will  be  like  I  (Fig.  140)  when  the  curve  for 


CONNECTION  BETWEEN  ~  AND  FREQUENCY.    439 

the  positive  carbon  alone  cored  is  higher,  with  low  frequencies 
than  that  for  the  negative  alone  cored,  and  like  II  (Fig.  140) 
when  it  is  lower. 

It  is  clear  from  these  curves  that,  with  cored  carbons,  the 

8V 
frequency  with  which  —  first  becomes  positive,  when  its  normal 

value  is  negative,  may  be  very  low  indeed ;  and  that  when  its 
normal  value  is  positive,  as  for  instance,  with  currents  over 
6  amperes  in  such  curves  as  those  for  Omm.  and  1mm.  (Fig  40) 

£V 

—  may  never  become  negative  with  any  frequency.     This  is 
oA. 
just  what  Messrs.  Frith  and  Rodgers  found  by  direct  measure- 

OTT 

ment  of  —  ;  for  they  could  get  no  negative  value,  with  any 

SA 

frequency,  when  the  P.D.  between  the  carbons  was  35  volts, 
and  the  direct  current  was  10  amperes,  with  cored  positive  and 
solid  negative  Brush  carbons  ;  while  with  some  other  currents 

8V 
and   lengths    of    arc   they   found   —    negative    with    smaller 

UJ\. 

frequencies  than  1*8  per  second,  and  positive  with  larger,  and 
with  yet  others  it  was  negative,  even  with  frequencies  of  250 
per  second.  Their  experiments  showed,  then,  that  with  a 
superimposed  alternating  current  of  constant  root  mean  square 

CNTT 

value  and  frequency,  ^-  was  positive  or  negative,  with  cored 

oA. 

carbons,  according  to  the  value  of  the  direct  current  and  the 
length  of  the  arc.  But  we  have  seen  from  theoretical  con- 

8V 
siderations  that  both  the  value  and  the  sign  of  ^  must  depend 

on  these  two  variables,  not  with  cored  carbons  only,  but  with 
all  carbons. 

Thus,  all  the  principal  phenomena  of  the  arc,  with  cored 
and  with  solid  carbons  alike,  can,  with  one  exception,  to  be 
presently  alluded  to,  be  explained  as  natural  results  of  the 
variations  in  the  specific  resistances  of  the  material  in  the  gap 
that  must  exist,  together  with  the  observed  variations  in  its 
cross-sections.  It  is  quite  probable,  therefore,  that  there  is 
neither  a  large  back  E.M.F.  in  the  arc  nor  a  "  negative  resis- 
tance," but  that  its  resistance  follows  the  ordinary  ohmic  laws, 
obscured  only  by  the  varying  resistivities  of  its  different  parts, 
consequent  on  their  varying  temperatures  and  on  the  resultant 


440  THE  ELECTRIC  ARC. 

differences  in  their  physical  conditions.  There  is  only  one 
phenomenon  that  these  variations  do  not  explain,  viz.,  the  fall 
of  potential  between  the  arc  and  the  negative  carbon,  which  has 
been  shown  (p.  225)  to  vary  between  about  8-3  and  11  volts 
with  currents  over  4  amperes.  This  may  possibly  be  a  true 
back  E.M.F.,  which,  although  large  compared  with  that  of  an 
ordinary  cell  is  very  small  compared  with  that  which  has  been 
supposed  to  exist  in  the  arc. 


SUMMARY. 

I.  All  the  material  in  the  gap  between  the  carbons  of  an  arc 
cannot  remain  carbon  vapour ;  the  inner  part  must  cool  into 
carbon  mist  at  a  short  distance  from  the  crater,  which  is  the 
seat  of  volatilisation,  and  the  outer  part  must  burn  and  form 
a  sheath  of  flame  in  contact  with  the  air.      These  different 
materials  are  indicated  in  images  of  the  arc. 

II.  The  flame  has  a  very  high  specific  resistance  ;  the  film 
of  true  vapour  in  contact  with  the  crater  a  lower  one  ;  the 
carbon  mist  lowest  of  all.     Hence  the  current  flows  principally 
through  the  vapour  and  mist,  but  meets  with  much  greater 
resistance  in  the  thin  vapour  film  than  in  the  thicker  mass  of 
mist. 

III.  The  heat  of  the  crater  is  principally — perhaps  entirely — 
due  to  the  passage  of  the  current  through  the  high  resistance 
vapour  film  in  contact  with  it. 

IV.  The  end  of  the  positive  carbon  acquires  its  characteristic 
shape  through  a  race  between  the  volatilisation  of  a  portion  of 
its  end  surface  and  the  burning  of  the  remainder,  and  of  its 
sides.     The  negative  carbon  is  entirely  shaped  by  burning, 
and  by  deposit  from  the  carbon  mist. 

V.  The  area  of  the  crater,  including  both  the  part  that  is 
actually  being  volatilised  and  that  which  is  just  below  the 
temperature  of  volatilisation,  varies  with  the  current,  the  length 
of  the  arc,  and  the  time  that  has  elapsed  since  a  change  was 
made  in  either.      The  area  of   the  surface   of   volatilisation 
depends  on  the  current  alone. 

VI.  The  film  of  vapour   in   contact  with   the  crater  acts 
exactly  like  a  back  E.M.F. 


SUMMARY.  441 

VII.  With  solid  carbons  the   cross-sections  of   the  vapour 
film  and  the  mist  increase  more  rapidly  than  the  current. 
Hence,  the  resistance  of  the  arc  diminishes  more  rapidly  than 
the  current  increases,  which  gives  the  arc  the  appearance  of 
having  a  negative  resistance. 

VIII.  Both  the  resistance  of  the  arc  and  the  P.D.  between 
the  carbons  depend,  not  only  on  the  current  and  the  length  of 
the  arc,  but  also  on  how  lately  a  change  has  been  made  in 
either,  and  on  what  that  change  was. 

IX.  When  a  small  change  is  made  in  the  current,  it  is  only 
when  the  alteration  is  so  quick  and  so  small,  that  neither  the 
resistance  nor  the  back  E.M.F.  of  the  arc  (if  any)  is  changed 

rSV 
by  it  that—  is  a  true  measure  of  the  resistance  of  the  arc. 

oA. 

X.  When  the  resistance  of  the  arc  is  measured  by  super- 
imposing a  small  alternating  current  on  the  direct  current} 
the   alternating   current    must    have   a   frequency   of    many 
thousands  of  alternations  per  second  for  the  resistance  of  the 
arc  not  to  be  altered  by  it. 

XI.  When  the  alternating  current  affects  the  resistance  of 

CNTT 

the  arc,    --   may  have  any  value  between  a  large  negative 

oA 

limit  and  the  positive  limit  that  is  the  true  resistance  of  the 

OTT 

arc,  the  value  and  sign  of  —  depending  on  the  frequency  of 

oA. 

the  alternations. 

XII.  The  form  of  the  P.D.   time  curve  indicates  whether 
the   resistance   of  the   arc   is   affected  by  the  superimposed 
alternating  current  or  not. 

XIII.  Even  when  it  has  been  ascertained  that  the  super- 
imposed alternating  current  does  not  affect  the  resistance  of  the 
arc,  measures  must  be  taken  to  ^show  that  it  does  not,  either, 
affect  any  back  E.M.F.  that  may  exist,  before  the  average 

8V 
value  of  —  can  be  accepted  as  measuring  the  true  resistance 

oA 
of  the  arc. 

CORED  CARBONS. 

XIV.  There  are  two  ways  in  which  cores  in  the  carbonL 
affect  the  arc ;  they  alter  its  cross- section,  and  they  change 
the  specific  resistances  of  the  vapour  and  the  mist. 


442  THE  ELEGTRIG  ARG. 

XV.  When  the  sizes  of  the  carbons,  the  current,  and  the 
length  of  the  arc  are  all  constant,  the  cross-section  of  the  arc 
is  greatest  when  both  carbons  are  solid,  is  smaller  when  the 
negative  alone  is  cored,  smaller  still  when  the  positive  alone  is 
cored,  and  smallest  when  both  are  cored. 

XVI.  The    ordinary    commercial    core    being    composed   of 
carbon  mixed  with  metallic  salts,  the  resistivities  of  the  vapour 
and  mist  from  it  are  lower  than  from  solid  carbon,  and  this 
causes  a  diminution  of  the  resistance  of  the  arc  that  more  than 
compensates  for  the  increase  of  resistance  due  to  the  diminu- 
tion of  its  cross-section.     Hence  the  P.D.  is  lowered  by  a  core 
in  the  positive  carbon. 

XVII.  With  a  given  negative  carbon,  current,  and  length  of 
arc,  the  P.D.  between  the  carbons  depends  principally,  if  not 
entirely,  on  the  nature  of  the  carbon  that  forms  the  surface  of 
volatilisation,  being  higher  or  lower,  according  as  that  carbon 
is  more  or  less  free  from  metallic  salts. 

XVIII.  The  change  in  the  shape  of  the  P.D.  current  curve 
that  takes  place  when  a  cored  positive  carbon  is  substituted 
for  a  solid  one,  is  entirely  accounted  for  by  the  fact  that,  as 
soon  as  the  crater  more  than  covers  the  core,  the  volatilising 
surface  is  composed  of  two  different  substances,  the  proportions 
of  which  depend  upon  the  current. 

XIX.  A  core  in  either  carbon  influences  the  value  of  — - 

6A 

when  a  small  alternating  current  is  superimposed,  in  two  ways  : 
it  alters  the  amount  by  which  the  cross-section  of  the  vapour 
film  and  the  mist  change  as  the  current  changes,  and  it  makes 
their  specific  resistances  depend  upon  the  current. 

XX.  From  images  of  the  arc  and  carbons  taken  before  and 
after  changes  of  current,  it  is  deduced  that  coring  the  positive 
carbon  alone  has  no  effect  on  either  the  normal  or  the  non-normal 
change  of  cross-section  due  to  a  change  of  current.      Coring 
the  negative  alone  diminishes  both  changes,  and  also  retards 
the  change,  and  by  coring  both  carbons  both  these  effects  are 
intensified. 

XXI.  By  combining  the  two  changes  in  the  resistance  of  the 
arc  introduced  by  the  core — viz.,  that  due  to  the  difference  in 
the  changes  of  the  cross-sections  of  the  arc,  and  that  produced 
by  the  alterations  in  its  specific  resistance,  we  find  that  when 


SUMMARY.  443 

a  superimposed  alternating  current  alters  the  resistance  of  the 

SV 
arc,  —    is  more  positive  when  either  carbon  is  cored   than 

SA 

when  both  are  solid,  and  most  positive  when  both  are  cored. 

XXII.  With  solid  and  with  cored  carbons  alike  the  value  of 

$\\r 

—  depends  upon  the  magnitude   of  the  direct  current,  the 

oA 

length  of  the  arc,  and  the  frequency  ot  the  alternations. 

XXIII.  When  the  negative  carbon    is   solid,    whether   the 

f}V 

positive  is  solid  or  cored,  the  value  of  -—  becomes  more  positive 

oA 

RV 

as  A  increases  :  but  when  the  negative  carbon  is  cored,  — 

oA 

increases  positively  to  a  maximum  and  then  diminishes  again. 

8V 

XXIV.  With  all  four  sets  of  carbons,  when  A  is  constant,  — - 

SA 

diminishes  positively  to  a  minimum  as  the  arc  is  lengthened, 
and  then  increases  again, 

8V 

XXV.  The  frequency  with  which  —  first  becomes  positive 

oA 

is  smallest  when  both  carbons  are  cored,  smaller  when  the 
negative  alone  than  when  the  positive  alone  is  cored,  and 
greatest  when  both  are  solid. 

XXVI.  The   fall   of    potential   between   the   arc   and    the 
negative  carbon  is  probably  due  to  a  true  back  E.M.F. 


APPENDIX. 


I.— THE  APPARENT  AREA  OF  A  DISC. 

If  a  disc  is  looked  at  from  any  point — by  a  single  eye,  we 
will  suppose  for  the  sake  of  simplicity — the  rays  of  light  which 
make  it  visible  form  a  truncated  cone,  of  which  the  disc  is  the 
base  and  the  entrance  to  the  pupil  is  a  section.  When  the 
centre  of  the  pupil  is  in  the  line  which  is  at  right  angles 
to  the  disc  at  its  centre,  every  point  on  the  edge  of  the  disc  is 
at  the  same  distance  from  the  centre  of  the  pupil,  and  the  disc 
is  seen  as  a  circle.  When  the  line  joining  the  centres  of  the 
eye  and  the  disc  makes  any  other  angle  with  the  plane  of  the 
disc,  however,  the  disc  has  the  same  effect  on  the  eye  as  would 
be  produced  if  it  were  projected  on  a  plane  passing  through  its 
centre  and  perpendicular  to  the  line  joining  that  centre  to  the 
centre  of  the  pupil.  This  projection  is,  therefore,  the  apparent 
area  of  the  disc  when  looked  at  from  the  given  point.  The 
area  of  this  projection,  and,  therefore,  the  apparent  area  of  the 
disc,  must  depend  on  (1)  r,  the  radius  of  the  disc,  (2)  I,  the 
distance  between  the  centres  of  the  disc  and  the  pupil  of 
the  eye,  and  (3)  0,  the  angle  between  the  surface  of  the  disc 
and  the  plane  perpendicular  to  the  line  joining  the  centre  of 
the  eye  to  the  centre  of  the  disc.  The  apparent  area  of  the 
disc  in  terms  of  these  three  quantities  may  be  found  from 
Fig.  141. 

Let  ABC  be  the  disc,  which  may  be  considered  to  be  perpen- 
dicular to  the  plane  of  the  paper,  and  to  be  cut  by  that  plane 
through  one  of  its  diameters,  ADB.  Let  P,  a  point  in  the 
plane  of  the  paper,  be  the  point  from  which  the  disc  is  viewed, 
and  let  ePe'  be  the  diameter  of  the  pupil.  Draw  FDG  perpen- 
dicular to  PD.  Then  AD  =  DB  =  FD  =  DG  =  r,  PD  =  /,  and, 
since  AB  is  the  diameter  of  the  disc  that  intersects  the  plane 


446 


THE 


ARC. 


of  the  paper,  and  FG  is  the  line  in  which  the  plane  perpendi- 
cular to  PD  meets  the  plane  of  the  paper,  AB,  FG,  and  PD, 
are  all  in  this  same  plane,  and  GDB  being  the  angle  between 
the  disc  and  the  plane  through  the  centre  of  the  disc  perpen- 
dicular to  PD,  must  be  9.  Join  0A,  e'B,  and  let  eA.  meet  FG 
in  H,  and  produce  e'E  to  meet  FG  in  K.  Then  HK  is  the 
projection  of  AB  on  FG,  and,  since  AB  is  a  diameter  of  the 
disc,  HK  must  also  be  a  diameter  of  its  projection,  and,  being 
in  the  same  plane  as  PD,  HK  must  be  one  axis  of  the  ellipse, 
into  which  the  disc  ABC  is  projected,  and,  if  Q  be  taken 
bisecting  HK,  Q  (Fig.  142)  is  the  centre  of  the  ellipse. 


FIG.  141.— The  Apparent  Area  of  the  Disc  AEEC. 

Next,  let  EDO  be  that  diameter  of  the  disc  which  is  at  right 
angles  to  the  plane  through  PD— the  plane  of  the  paper.  Then, 
since  the  disc  is  projected  on  to  a  plane  which  also  cuts  the 
plane  of  the  paper  at  right  angles  through  D,  EDO  must  be 
common  to  the  disc  and  its  projection,  and  EDO  must  therefore 
be  a  chord  of  this  projection  which  is  bisected  at  right  angles 
by  PD.  Let  us  now  clear  off  all  unnecessary  lines,  and  deal 
only  (Fig.  142),  with  PD  the  line  joining  the  centre  of  the  eye 
to  the  centre  of  the  disc,  AB  the  diameter  of  the  disc  that  is  in 
the  same  plane  as  PD,  CDE,  the  chord  that  is  common  to  the 


THE  APPARENT  AREA  OF  A  DIM.  447 

disc  and  to  its  projection  on  the  plane  at  right  angles  to  PD, 
and  HQK,  an  axis  of  the  projection.  Thus  AB,  PD,  and  HK 
are  all  in  one  plane  (the  plane  of  the  paper),  and  CDE  is  at 
right  angles  to  that  plane. 

Since  HK  is  a  part  only  of  FG,  and  FG  =  CE,  which  is  a 
chord  of  the  projection  of  the  disc,  HK  must  be  the  minor 
axis  of  the  projection.  With  centre  Q,  and  radius  QH  (half 
the  minor  axis),  describe  a  circle  cutting  DC  at  R.  Draw  SQ 
perpendicular  to  HK,  making 

SQ  :  QH  ; ;  DC  :  DR. 


FIG.  142.— The  Apparent  Area  of  a  Disc. 

Then,  by  a  well-known  property  of  the  ellipse,  SQ  is  half  the 
major  axis  of  the  ellipse  which  is  the  projection  of  the  disc, 
and  we  can  now  find  the  area  of  this  ellipse  in  terms  of  r,  I 
and  0.  For,  draw  AM  and  BN  both  parallel  to  HK.  Then, 
by  similar  triangles, 

HD=PD=       PD 

AM~PM~PD  +  DM' 

But  AM  =  r  cos  0,     DM -r  sin  (9,     andPD  =  /; 

lr  cos  6 


448  THE  ELECTRIC  ARC. 

T.  ,r       IT  cos  0 
Similarly,  DK  = 


Thus,  if  we  call  the  major  and  minor  axes  of  the  ellipse  2a 

and  2&,  we  have 

Pr  cos  6 


Also  «  :  6  : :  DC  :  DR  : :  r  :  DR, 

and,  since  HRK  is  a  semicircle, 

ft*  cos2  0 


\/Z2  -  ?*2  sin2  0 
IT  cos  0 

*         ft     *    r)     *   *     7*    *    — 

7  _         r^3  COS  ^ 

~  (I2  -  r*  sin2  0)1' 
and  Trftb,  which  is  the  area  of  the  ellipse,  is 

77T2Z3  COS  0 

If  I  is  great  compared  with  r,  this  becomes 

7JT2  COS  0. 

Thus,  when  the  distance  of  the  eye  from  the  disc  is  great 
compared  with  the  radius  of  the  disc,  the  apparent  area  of  the 
disc  varies  as  the  cosine  of  the  angle  it  would  have  to  be 
turned  through  to  make  its  plane  perpendicular  to  the  line 
joining  the  eye  to  its  centre.  This  angle  Mr.  Trotter  calls  the 
inclination,  so  that  we  may  say  that  the  apparent  area  of 
the  crater  varies  as  the  cosine  of  its  inclination,  since  the 
radius  of  the  crater  is  always  small  compared  with  its  distance 
from  the  eye. 

II.— PHOTOMETRY. 

Several  assumptions  are  made  in  all  photometry,  and  it  is 
well  to  have  a  clear  understanding  of  what  these  are. 

The  eye  is  incapable  of  judging  of  quantity  of  light,  it  can 
only  appreciate  intensity — brightness — the  quantity  of  light 


METHODS  OF  MEASURING  BRILLIANCY.          449 

emitted  per  unit  area  of  the  source.  Even  of  this,  it  can  only 
judge  within  very  narrow  limits ;  for  if  two  sources  have  both 
more  than  a  certain  intensity  the  eye  is  equally  dazzled  by 
both  and  incapable,  therefore,  of  distinguishing  which  is  the 
brighter.  For  this  reason  it  is  our  habit  to  judge  of  the 
intensity  of  a  source  of  light  not  by  regarding  the  source 
itself,  but  by  looking  at  surfaces  illuminated  by  it.  When 
one  part  of  a  street,  for  instance,  is  lighted  by  an  arc  lamp 
and  another  by  a  gas  jet,  we  realise  the  brightness  of  the  pave- 
ments and  walls  lighted  by  the  arc  compared  with  the  dullness 
of  the  parts  illuminated  by  the  gas-jet  rather  than  the  brilliancy 
of  the  arc  itself  compared  with  the  dimness  of  the  gas-jet. 

In  the  scientific  measurement  of  light  we  do  not  depart 
from  this  accustomed  method  of  comparing  the  intensity  of 
two  sources.  The  sources  are  placed  so  that  the  rays  they 
send  out  in  given  directions  are  perpendicular  to  adjacent 
portions  of  a  small  plane  surface.  If  the  sources  are  small 
and  are  sufficiently  far  from  the  surface,  they  may  be 
considered  to  be  points  of  light,  and  if  the  surface  is  also  small 
all  the  rays  may  be  considered  to  be  perpendicular  to  it.  When 
the  distances  between  the  sources  and  the  surface  are  such 
that  the  two  parts  of  the  surface  appear  equally  bright — that 
is,  when  they  are  emitting  or  transmitting  equal  quantities  of  light 
per  second  per  unit  area — we  assume  that  they  are  receiving  equal 
quantities  also.  When  the  two  sources  of  light  are  of  the 
same  kind  and  at  the  same  temperature  the  assumption  is 
perfectly  justifiable,  for  then  the  screen  will  absorb  the  same 
percentage  of  the  light  it  receives  from  each  source,  and  all 
other  objects  on  which  the  two  lights  fall  will  do  the  same. 
When  the  temperatures  of  the  two  sources  are  widely  different, 
however,  there  will  be  a  difference  in  the  percentage  of  the 
light  of  each  absorbed,  depending  on  the  nature  of  the  surface, 
and  hence  the  apparent  relative  candle-powers  of  the  sources 
will  differ  according  to  the  nature  of  the  photometer  screen 
employed,  and  the  relative  brightness  of  all  objects  illuminated 
by  the  two  sources  will  vary  with  the  object.  This  is  probably 
the  reason  for  the  strong  objection  entertained  by  some  people 
to  "  mixed  lights."  The  relative  brightness  of  objects  is  altered 
by  such  a  mixture,  and  this  produces  an  unpleasant  feeling  of 
confusion, 

GO 


450  THE  ELECTRIC  ARC. 

In  measuring  the  relative  illuminating  powers  of  different 
sources  of  light,  however,  we  disregard  this  source  of  error,  and 
assume  that  the  quantity  of  light  received  by  the  eye  from 
each  unit  area  of  the  photometer  screen  is  directly  pro- 
portional to  the  quantity  transmitted  to  that  area  from  the 
source  of  light.  The  quantity  thus  transmitted  has  been 
found  experimentally  to  vary  inversely  as  the  square  of  the 
distance  between  the  source  and  the  photometer  screen. 
Thus,  if  we  take  some  particular  source  of  light  as  our 
standard  source,  and  call  the  quantity  of  light  received  from 
it  in  some  definite  direction  on  a  unit  area  of  a  screen  placed 
at  right  angles  to  its  rays  at  unit  distance,  the  unit  of 
illuminating  power,  we  can  express  the  illuminating  power 
in  any  one  direction  of  any  source  in  terms  of  these  units, 
and  so  can  measure  the  illuminating  power  of  a  source  in 
all  directions.  In  measuring  the  illuminating  power  of  a 
source,  therefore,  what  we  really  measure  is  the  quantity  of 
light  per  unit  area  emitted  by  a  special  surface  on  which 
the  light  from  the  source  falls,  and  we  measure  this  solely  by 
its  physiological  effect  on  the  eye. 

If  a  source  emits  its  light  equally  in  all  directions,  its 
illuminating  power  in  any  one  direction  may  be  called  the 
illuminating  power  of  the  source,  for  it  tells  you  how  much 
light  you  can  get  from  the  source  in  any  single  direction. 
The  total  quantity  of  light  emitted  by  the  source  can  be  found 
by  multiplying  its  illuminating  power  by  47r.  For  if  it  be 
considered  as  a  point  of  light  placed  at  the  centre  of  a  hollow 
sphere  of  unit  radius,  the  illuminating  power  is  the  quantity 
of  light  falling  on  unit  surface  of  this  sphere,  and  the  total 
light  emitted  is  the  amount  falling  on  its  whole  surface. 
Therefore 
illuminating  power  :  total  light  ; :  unit  area  :  surface  of  sphere 

::l:47r; 
or  4:7r  x  illuminating  power  —  total  light  emitted. 

In  most  sources  of  light  different  quantities  are  emitted  in 
different  directions,  i.e.,  illuminating  power  varies  with  direc- 
tion, and  it  becomes  a  question,  What  is  the  illuminating 
power  of  such  a  source  ?  It  is  evident  that  we  cannot  take  the 
illuminating  power  in  any  one  direction  as  the  illuminating 


COMPARISONS  OF  ILLUMINATING  POWERS.       451 

power  of  the  source,  for  in  that  case  we  might  make  the 
illuminating  power  anything  we  liked  within  given  limits,  and 
there  would  be  no  possibility  of  comparing  the  relative  values 
of  two  different  sources.  It  has  been  suggested  that  the 
illuminating  power  of  each  source  in  the  direction  in  which  it 
is  a  maximum  should  be  taken,  but  this  would  not  make  a  fair 
comparison,  because  for  one  of  the  sources  the  illuminating 
power  might  have  the  maximum  value  in  many  more  directions 
than  in  the  other ;  and  the  test  would  not  show  this,  so  that 
the  light  having  a  slightly  greater  maximum  would  be  chosen 
as  the  best,  whereas  that  having  a  lower  maximum  in  many 
more  directions  would  really  be  the  more  valuable.  The 
only  fair  way  is  to  compare  the  total  quantity  of  light 
emitted  by  the  two  sources,  or  the  mean  illuminating  power 
of  each,  which  is,  of  course,  the  total  quantity  divided  by  47r. 
This  mean  illuminating  power  is,  therefore,  the  illuminating 
power  that  the  source  would  have  in  any  one  direction  if 
it  emitted  exactly  the  same  quantity  of  light  as  it  actually 
does,  but  equally  in  all  directions.  As  a  special  candle  is 
usually  taken  as  the  standard  source  of  light,  the  mean 
illuminating  power  of  a  source  is  generally  called  its  mean 
spherical  candle-power,  but  it  must  not  be  forgotten  that  this 
is  a  quantity  of  light — the  quantity  of  light  that  falls  from 
the  standard  candle  in  a  horizontal  direction  on  a  unit 
area  of  a  surface  placed  at  right  angles  to  its  rays  at  unit 
distance. 

There  are  two  ways  of  measuring  the  mean  illuminating 
power  of  a  source  of  light.  The  whole  or  some  definite  propor- 
tion of  the  light  may  be  collected  and  then  diffused  equally  in 
all  directions,  so  that  the  mean  illuminating  power  can  be 
found  by  one  measurement.  This  is  the  method  adopted  by 
Profs.  Ayrton  and  Blondel.  The  more  usual  plan  is,  however, 
to  measure  the  illuminating  power  in  many  different  directions, 
and  from  these  to  find  the  mean.  The  first  method  is  of  great 
value  when  employed  as  it  was  by  Profs.  Ayrton  and  Blondel 
to  find  out  how  the  mean  illuminating  power  of  the  arc  was 
affected  by  changes  in  its  length  and  in  the  current  flowing  : 
but  it  would  be  worthless  if  employed  to  test  the  relative 
values  of  two  totally  different  sources  of  light.  For  while  a 
knowledge  of  the  way  in  which  the  light  was  distributed 


452  THE  ELECTRIC  ARC. 

would  not  be  necessary  for  the  first  comparison,  seeing  that 
the  distribution  in  the  arc  would  be  practically  unaltered  by 
changes  in  its  current  and  length,  in  the  second  case  the  test 
would  only  be  half  made  when  the  mean  spherical  candle 
powers  of  the  two  sources  had  been  determined,  because  the 
relative  value  of  the  two  sources  might  depend  quite  as  much 
on  the  distribution  of  the  light  in  each  as  on  their  mean 
spherical  candle-powers.  For  this  reason,  in  comparing  two 
sources  of  light  of  different  kinds,  it  would  always  be  better 
to  employ  the  second  method. 

III.  —  THE  MEAN  SPHERICAL  CANDLE  -  POWER 
OF  THE  ARC— ROUSSEAU'S  FIGURES— POLAR 
LIGHT  CURVES. 

In  the  ordinary  vertical  arc,  if  the  carbons  are  well  in  line, 
if  the  circuit  is  so  arranged  thfbt  the  current  in  the  wires  has 
no  inductive  effect  on  the  arc,  and  if,  also,  the  light  is  unob- 
structed in  all  directions,  then  the  light  emitted  will  be  fairly 
symmetrical  round  the  vertical  axis  of  the  two  carbons.  The 
following  very  pretty  method  of  finding  the  mean  illuminating 
power  of  such  an  axially  symmetrical  source  of  light,  when 
its  illuminating  power  in  many  directions  in  a  vertical  plane 
passing  through  the  centre  of  the  source  has  been  measured, 
was  devised  by  M.  Rousseau.* 

Archimedes  proved  that  the  area  of  a  zone  of  a  sphere 
intercepted  between  two  parallel  planes  perpendicular  to  its 
axis  was  equal  to  the  area  of  the  belt  of  the  circumscribing 
cylinder  intercepted  between  the  same  two  planes.  Thus  if 
A'E'G'C'  (Fig.  143)  be  a  sphere,  and  AEGC  its  circumscribing 
cylinder,  the  area,  A'E'G'C',  of  the  zone  of  the  sphere  inter- 
cepted between  the  two  planes  ABCD,  EFGH,  is  equal  to  the 
belt,  AEGC,  of  the  cylinder— that  is,  to  2;rrCG,  where  r  is 
the  radius  of  the  sphere. 

Suppose,  now,  that  the  sphere  was  hollow,  and  that  the 
centre  of  the  mouth  of  the  crater  of  an  arc  were  at  0,  its  centre. 
Then  OA  (Fig.  144)  would  represent  the  axis  of  the  carbons. 
Let  the  lengths  of  the  lines  OB,  OC,  OD,  &c.,  be  proportional 
to  the  illuminating  powers  of  the  arc  in  directions  OB,  OC, 
OD,  &c.  Then  OB  represents  the  quantity  of  light  that  falls 


MEAN  SPHERICAL  CANDLE-POWER. 


453 


on  unit  area  of  the  sphere  in  the  direction  OB,  so  that,  if  OB 
be  continued  to  meet  the  sphere  at  E,  the  quantity  of  light 
falling  on  a  small  element  of  the  sphere  at  E  is  OB  times 


+O 


FIG.  145. — Zone  of  Sphere  and  Belt  of  Circumscribing  Cylinder  cut  oft'  by 
Parallel  Planes. 

the  area  of  that  element.  Also,  since  the  arc  emits  the  same 
amount  of  light  in  all  the  directions  that  make  an  angle  BOA 
with  the  axis  of  the  carbons,  the  quantity  of  light  falling  on 


A  R 

FIG.  144. — Rousseau's  Figure  for  Finding  the  Mean  Spherical  Caudle- 
Power  of  an  Axially  Symmetrical  Source  of  Light,  when  the  Illuminating 
Powers  in  a  Number  of  Directions  in  One  Plane  are  known. 


454  THE  ELECTRIC  ARC. 

the  thin  zone  of  the  sphere  intercepted  between  the  planes 
FH  and  GK  will  be  OB  times  the  area  of  that  zone,  i.e., 
OB  .  27rr .  HK,  where  r  is  the  radius  of  the  sphere.  Now  make 
HM  =  OB,  and  complete  the  parallelogram  HMNK.  Then  the 
total  quantity  of  light  emitted  by  the  arc  in  all  the  directions> 
that  make  an  angle  BOA  with  the  axis  of  the  carbons  is  2?rr 
times  the  area  HMNK,  where  HM  and  KN  are  infinitely  near 
together.  Now  let  a  curve  PMQR  be  drawn  on  any  line 
PR  parallel  to  the  axis  of  symmetry,  such  that,  for  every 
point  B  there  is  a  corresponding  point  M,  where  HM  =  OB. 
Then  the  total  light  emitted  by  the  arc  will  be  2?rr  times  the 
area  of  the  figure  PMQR,  for  this  area  includes  all  the 
elements  of  area  similar  to  HMNK.  To  find  the  average 
quantity  of  light  falling  on  unit  area  of  the  sphere,  we  must 
divide  this  quantity,  2irr  x  area  PMQR,  by  the  area  of  the 
sphere,  i.e.,  by  4;rr.  Therefore,  the  mean  illuminating  power 
of  the  arc,  or  its  mean  spherical  candle-power,  when  the 
candle-power  is  the  unit  of  illuminating  power  employed,  is 

27rrxarea  PMQR 

47T7- 

or  half  the  area  PMQR. 

It  is  customary,  when  the  illuminating  power  of  the  arc 
has  been  measured  in  many  directions  in  one  plane,  and  lines 
similar  to  OB,  OC,  &c.  have  been  drawn  representing  those 
illuminating  powers,  to  draw  a  curve  through  the  ends  of 
those  lines,  so  that  by  means  of  half  a  dozen  measurements 
the  illuminating  power  in  any  direction  can  be  found.  These 
are  the  polar  light  curves,  of  which  examples,  drawn  by 
Mr.  Trotter,  are  given  in  Figs.  91  and  92.  There  is  an 
erroneous  idea — so  widespread  that  it  is  essential  to  correct 
it — that  the  area  of  this  curve,  or  the  solid  contents  of  its 
figure  of  revolution  about  the  axis  of  the  carbons,  represents 
the  mean  spherical  candle-power  of  the  arc. 

Before  examining  why  this  idea  is  wrong,  a  small  practical 
demonstration  of  its  impossibility  may  be  given.  Lefc  OABC 
(Fig.  145)  be  a  polar  light  curve,  so  that  OA  is  proportional 
to  the  illuminating  power  of  the  arc  in  the  direction  OA, 
OB  in  the  direction  OB,  &c.  Now,  suppose  the  arc  to  be 
replaced  by  another  which  has  exactly  half  the  candle-power 


POLAR  LIGHT  CURVES. 


455 


of  the  first  in  each  direction.  Then  it  must  have  half  the 
mean  spherical  candle-power  of  the  first  also.  To  obtain  the 
new  polar  light  curve,  we  must  halve  each  radius  vector  of 
the  old  so  that  the  new  curve  is  OA'B'C',  where  OA  =  20A', 
OB  =  20B',  00  =  200',  &c.  But  the  area  of  this  new  curve 
is  plainly  not  equal  to  half  the  area  of  the  old,  as  it  should  be 
if  it  were  proportional  to  the  mean  spherical  candle-power  of 
the  arc,  but  to  a  quarter  of  that  area ;  and  still  less  would  the 
solid  contents  of  the  figure  of  revolution  of  OA'B'C7  round 
the  axis  OP  be  half  the  contents  of  the  figure  of  revolution 
of  OABC.  It  is  quite  evident,  therefore,  that  neither  the  area 
of  the  polar  light  curve,  nor  the  solid  contents  of  its  figure 
of  revolution  round  the  axis  is  proportional  to  the  mean 
spherical  candle-power  of  the  arc ;  and  this  is  the  reason. 


FIG.  145.  —  Polar  Light  Curves  of  Two  Similar  Sources,  the  one  having 
twice  the  Illuminating  Power  of  the  other. 

The  mean  illuminating  power  of  a  source  of  light  is  the 
total  amount  of  light  that  would  be  received  from  it  on  the 
inner  surface  of  a  hollow  sphere  of  which  it  occupied  the 
centre,  divided  by  the  area  of  the  surface  of  the  sphere.  For 
the  numerator  of  this  ratio  —  the  total  light  that  falls  on  the 
surface  of  the  sphere  —  we  have 


where  LI}  L2,  L3,  &c.,  are  the  quantities  of  light  falling  on 


the  elements,  av  «2,  «3, 
the  sphere  we  have 


.,  of  the  sphere.     For  the  area  of 


456  THE  ELECTRIC  ARC. 

and  thus  for  the  mean  illuminating  power  we  have 


Now,  each  radius  vector  of  the  curve  OABC  gives  us  L  for 
the  direction  in  which  it  is  drawn,  but  we  cannot  get  a 
from  this  curve  without  drawing  the  Rousseau  figure  already 
described,  for  a  is  an  element  of  the  surface  of  a  sphere,  and 
the  surface  of  the  figure  of  revolution  of  OABC  about  OP  is 
by  no  means  a  sphere.  It  is  through  confusing  the  area  of 
this  figure  with  the  area  of  the  sphere  on  which  the  light 
must  fall,  in  order  that  the  measurements  of  the  light  in 
different  directions  may  be  comparable  with  one  another,  that 
the  error  has  arisen  of  supposing  that  the  solid  contents  of 
this  figure  was  proportional  to  the  mean  illuminating  power 
of  the  source.  All  that  can  be  found  out  about  the  light  from 
the  polar  light  curve  alone  is  the  actual  illuminating  power  of  the 
source  in  each  separate  direction,  but  not  its  mean  illuminating 
power. 

Another  fallacy  that  has  arisen  concerning  these  light  curves 
is  the  idea  that  the  Rousseau  figure  simply  gives  the  mean 
spherical  candle-power  plotted  to  rectangular  co-ordinates. 
As  there  is  only  one  mean  spherical  candle  power  for  each 
source  of  light  and  one  Rousseau's  figure  likewise,  there  can 
be  no  "plotting  to  rectangular  co-ordinates  "  in  the  case.  The 
area  of  the  Rousseau  figure  for  each  arc  represents  the  mean 
spherical  candle-power  of  that  arc. 

IV.—  CANDLE  AND  GAS  SHADOW  EXPERIMENTS. 

When  the  light  of  an  arc  is  sent  through  a  candle  or  gas 
flame  the  lens  effect  is  still  more  marked  than  when  the  crater 
light  is  simply  reflected  back  through  the  arc  itself,  for  the 
rim  of  light  round  the  shadow  is  far  brighter,  and  parts  of  the 
candle  flame  shadow  are  deeper. 

Fig.  146  is  taken  from  a  photograph  of  the  shadow  of  a 
candle  flame,  and  shows  very  well  the  various  degrees  of 
darkness  and  brightness  of  the  shadow  and  its  rim.  The 
darkest  part  of  the  shadow  (a)  corresponds  with  the  brightest 
part  of  the  flame  ;  (b),  which  corresponds  with  the  dark  part 
of  the  flame  round  the  wick,  which  we  know  to  consist  of 


THE  SHADOW  OF  A  CANDLE  FLAME. 


457 


unburnt  gases,  is  bright,  showing  that  the  flame  is  a  convex  lens 
denser  than  the  surrounding  material.  Eound  the  whole  of  this 
bright  portion,  and  the  true  shadow  of  the  flame,  is  another 
much  larger,  fainter  shadow  of  very  definite  form,  and  it  is 
this  fainter  shadow  that  is  surrounded  by  the  rim  of  light 
previously  mentioned.  This  outer  shadow  is  not  that  of  the 


-<-(&) 


FIG.  146.— Photograph  of  Shadow  of  Candle  Flame. 

flame,  as  may  easily  be  ascertained,  by  running  the  point  of 
a  thin  carbon  rod  round  the  outline  of  the  flame,  and  noting 
where  this  point  comes  in  the  shadow.  It  will  be  found  that 
in  all  cases  the  point  is  inside  the  outer  shadow,  and  that  it 
just  touches  the  inner  darker  one.  If  a  small  piece  of  cold 
glass  is  held  anywhere  within  the  region  that  casts  the  outer 
shadow,  it  will  be  found  to  be  immediately  covered  with  a 


458  THE  ELECTRIC  ARC. 

thin  film  of  moisture,  while  if  held  outside  this  region  it 
remains  bright.  It  is  probable,  therefore,  that  the  outer 
shadow  is  produced  by  the  water  vapour  that  is  evolved  by  the 
burning  of  a  flame,  and  the  definiteness  of  the  shadow  shows 
that  this  water  vapour  forms  an  envelope  round  the  flame  of 
perfectly  definite  shape  and  thickness. 

It  is  astonishing  to  see  to  what  a  distance  on  either  side 
and  above  it  the  flame  is  surrounded  by  a  steady  envelope 
of  vapour.  As  Fig.  146  shows,  the  envelope  touches  the  wax 
at  the  bottom,  then  bulges  out  so  that  it  is  as  wide  as  or  wider 
than  the  diameter  of  the  candle ;  and  it  extends  upwards  to 
some  five  or  six  times  the  length  of  the  flame,  before  any 
evidence  of  convection  currents  is  given.  One  wonders  what 
is  the  path  of  the  fresh  air  to  the  wick,  as  there  is  no  indica- 
tion of  it  in  the  shadow. 

The  limits  of  the  vapour  envelope  round  a  gas  flame  are  as 
definite  on  the  outside  as  those  round  a  candle  flame,  but  the 
gas  flame  has  no  separate  shadow  of  its  own  to  mark  the 
inner  boundary  of  the  envelope.  Indeed,  if  the  flame  of  a 
gas  jet  be  gradually  turned  down  so  low  that  all  the  light- 
giving  part  is  extinguished,  and  only  a  small  blue  bead  of 
light  is  left,  there  is  nothing  in  the  shadow  to  note  when  the 
light-giving  part  of  the  flame  ceases  to  exist ;  but  the  small 
blue  flame  gives  an  astonishingly  long  column  of  water  vapour, 
which  casts  a  long  narrow  shadow,  surrounded  by  the  usual 
rim  of  light. 


SUPPLEMENTARY  LIST  OF  ORIGINAL  COMMUNICATIONS  CONCERNING 

THE  ARC.* 

Ann.  Sci.  Lomb.  Vencto,  1844,  Vol.  XIII,,  pp.  107,  169  ZANTBDESCHI. 

Venczia.  Atti.,  1846,  Vol.  V.,  p.  519      ZANTEDESCHI. 

Annalidi  Fisica.,  1849-50,  Vol.  I.,  pp.  57,  71,  81,  83, 

87, 141          ZANTEDESCHI. 

Wien  Sitzunysberichte,  1856,  Vol.  XXI.,  p.  236           ...  ZANTEDESCHI. 

Philosophical  Transactions,  1881,  Vol.  CLXXIL,  p.  890  ABNEY. 

Wiedemann's  Annalen,  1882,  Vol.  XV.,  p.  514            ...  EDLUND. 

The  Electrician,  1889,  Vol.  XXII.,  pp.  534,  568, 596,  627  THOMPSON. 

*  The  Italian  references  heading  this  list  were  kindly  brought  to  my 
notice  by  Mr.  G.  Griffith,  and  many  of  the  remainder  by  Mr.  Du.Me.ll. 


ORIGINAL  COMMUNICATIONS. 


459 


The  Electrical  Review,  1892,  Vol.  XXXI.,  p.  728        ... 
Engineering,  Vol.  LVL,  pp.  144,  223,  254        ...... 

Lightning,  1894,  Vol.  VI.,  pp.  260,  298,  339    ...... 

Comptes  Rendus,  1894,  Vol.  CXIX.,  p.  728       ...... 

.L'Eclairage  Electrique,  1894,  Vol.  I.,  p.  474  ...... 

The  Electrician,  1895,  Vol.  XXXIV.,  pp.  335,  364,  399, 

471,  541,  610  ;  1895,  Vol.  XXXV.,  pp.  418,  635, 

743  ;  1895,  Vol.  XXXVI.,  pp.  36,  225  ;  1896,  Vol. 

XXXVL,  p.  539      ............... 

Proceedings  of  the  Koyal  Society,  1896,  Vol.  LVIIL, 

p.  24  ..................... 

La  SocieteFrancaisede  Physique,  1896,  July  17th,  p.243 

La  Societe  Franchise  de  Phy  sique,  1897,  Feb.  19th,  p.  12 
The  Electrician,  1897,  Vol.  XL.  ,  p.  326  ...... 

L"  Industrie  Electrique,  1897,  July  10th,  p.  273          ... 
Report  of  the  British  Association,  1897,  p.  575          ... 


OLIVETTI. 
BLONDEL. 

FLEMING. 

THOMAS. 

SAHULKA. 


H.  AYRTON. 
WILSON  &  GRAY. 


Wiedemann's  Annalen,  1898,  Vol.  LXIV.,  p.  233       ... 
L'Eclairage  Mectrique,  1898,  Vol.  XV.,  p.  49  ... 

The  Physics  Review,  1898,  Vol.  VII.,  p.  210    ...... 

Proc.  Amer.  Acad.  of  Arts  and  Sciences,  1898,  Vol. 

XXXIII.,  No.  18     ............... 

Report  of  the  British  Association,  1898,  p.  805          ... 
The  Electrician,  1899,  Vol.  XLIV.,  p.  16         ...... 

Elektrotechnische  Zeitschrift,  1899,  Vol.  LXVL,  p.  264. 
Journal  of  the  Institution  of  Elec.  Eng.,  1899,  Vol. 

XXVIII,  p.  400      ............... 

Rapport  du  Congres  Internationale  d'Electricite,  1900 

p.  250  .................. 

Journal  of  the  Institution  of  Elec.  Eng.,  1900,  Vol. 

XXX.,  p.  232  ............... 

L'Eclairage  Electrique,  1901,  Vol.  XXVII.,  p.  379  ... 
Proceedings  of  the  Royal  Society,  1901,  Vol.  LXVIII., 

p.  410  .................. 

Proceedings  of  the  Royal  Society,  1901,  Vol.  LXVIII., 

p.  512  .................. 

Bulletin  de  la  Societ6  Internationale  des  Electriciens, 

1901,  p.  251  .................. 

Revue  Generale  des  Sciences,  1901,  pp.  612,  659  ... 


GUILLAUME. 

GUILLAUME. 
H.  AYRTON. 

SIMON. 

HESS. 

BROWN. 

CREW&BASQUIN 
H.  AYRTON. 
JARVIS  SMITH. 
WEDDING. 

H.  AYRTON. 
H.  AYRTON. 

DUDDELL. 
CORBINO  &  LIGA. 

H.  AYRTON. 
DUDDELL. 

JANET. 
BLONDEL. 


INDEX  TO  CONTENTS. 


Alt.  =  Alternating. 
C.     =  Cored. 
Const.  =  Constant. 
Cur.   —  Current. 


ABBREVIATIONS. 

Expts.  —Experiments. 

I.      =  Length  of  Arc. 
Max.   =  Maximum. 
Min.   =  Minimum. 
Neg.    =  Negative. 


Pos.   =  Positive. 
Res.   =  Resistance. 

S.     =  Solid. 
Temp.  =  Temperature. 


Abney,  64,  314,  346,  359,  458 
Absorption  of  Light  by  Arc,  349,  sqq. 
„  „  „       and  1, 360 

„  „  Candle  Flame,  350, 

456 

Gas  Flame,  458 

Air  Blown  at  Crater,  303,  305,  307 
„   Cause  of  Hissing,  299,  305,  308 
,,    Cur.,  Oscillatory,  with  Hissing  Arc,  309 
,,   Touching  Crater,  Effect  of,  299 
Alternating  Current,  Added ,  Affecting  Arc, 

50,  55,  78,  406 
Alternating  Current,  Added,  Affecting  Arc, 

Tests  for,  414,  416 
Alternating  Current,  Added,  Affecting  Back 

E.M.F.,  416 
Andrews,  38,  95 

Apparatus  for  Measuring  Light,326,327,331 
Apparatus   for    Measuring   P.D.   between 

Carbons  and  Arc,  208 

Appearance  of  Arc,  1,  25,  26,  27,  31,  60,  68, 

277,292,300,356,358 

„  „         with  C.  &  S.  Carbons 

Compared,  6,  15,  419 

„  „         with  Hissing,  68,  277, 

292,  300 
Arago,  27,  94 
Arc,  Absorption  of  Light  by,  349,  sqq. 

and  I,  360 

Added  Alt.  Cur.  Affecting,  50,55,78,406 
Added  Alt.  Cur.  Affecting,  Test  for,414 
Appearance  of,  See  Appearance  of  Arc 
Back  E.M.F.  of,  See  Back  E.M.F. 
Blowing  on,  65,  305 
in  Carbon-dioxide,  38.  65,  83,  87 
in  Carbon-monoxide,  65 
Carbon  Particles  in,  84,  349 
and  Carbons,  Colours  of,  4 

„         Contact   Resistance   be- 
tween, 43,  50,  51 
Diagrams  of,  3,  9,  10, 12, 
15,  16,  293,  295,  318, 
319,324,336,340,365, 
376,379,418 
.,         P.D.  between,  See  P.D. 


Arc  and  Carbons,  Res.  between,  43,  50,  51, 

88,  392 

„     in  Chlorine,  65 
.,     Compared   with   Vacuum    Discharge, 

37,44 

„     Conductivity  of,  57,  71,  392 
„     with  Const.  E.M.F.,  241,  sqq.,  265 

„      P.D.,  167,  171,  172,  250 
„     Contact  Resistance  between,  43,  50,  51 
„     Cooling  of,  86 
„     Cross  Section  of,  See  Cross  Section  of 

Arc 

„     Dark  Spaces  in,  5,  6,  7,  81 
„     DeEected  by  Magnet,  27,  33 
,,     Disturbance  of,  by  Third  Carbon,  58, 

210,  228 
„     Duration  of,  after  Cessation  of  Cur.,  35, 

39,  64,  84,  89,  91 
„     and  Electric  Spark,  20 

Electrolytic  Theory  of,  30,  62,  66,  90 
Enclosed,  See  Enclosed  Arc 
Formation  of,  391 

,.  Carbon  Mist  in,  392 

,,  Gaseous  Envelope  of,  392 

„  „  Vapour  Film  in,  392 

„     in  Gases,  various,  30,  45,  65,  83 
„     Graphical  Study  of  Conditions  of,  241 
,     Green  Flame  of,  5,  6,  57,  60,  68,  392 

High  Res.  of,  392 
„     Hissing,  See  Hissing  Arc 
,,     History  of,  19,  sqq. 
„     Horizontal,  Shape  of,  26,  36 
,.     Humming,  69,  277,  292,  300 
„     in  Hydrocarbon  Gas,  65 
„     in  Hydrogen,  30,  38,  45,  65,  83 
„     Internal  Pressure  of,  40 
„     Inverted,  47,  81 
„     Lamp,  Hand-regulated,  98 
„     Lamps,  Commercial,  383 
„         „         in  Series,  387 
„     Length  of,  Sec  Length  of  Arc 
,,     Melting  of  Substances  in,  26 
„     with  Metallic  Salts,  31,  46,  56,  78 

Mist,  See  Mist 
„    Neg.  Res  of,  54,  75,  78,391,  400,  406 


INDEX  TO  CONTENTS. 


Arc  in  Nitrogen,  45,  65 
„     Normal,  Definition  of,  104 

„        and    Non-normal,    285,   299, 

419,  421,  425,  426 
„    in  Oxygen,  23,  65,  83 
„     with  Parallel  Carbons,  36 
„     under  Pressure,  67,  72,  83 
„    Purple  Core  of,  2,  5,  6,  7,  57,  356,  392 
„     Ratio  of  Volume  to  Cross  Section,  395 
„     Refraction  of  Light  by,  353 
„     Resistance  of,  Sec  Resistance 
„  „  in  Series  with,  See  Resis- 

tance 

„    Rotation  of,  69.  277,  292,  300,  322 
„  „  at' Pole  of  Magnet,  29 

,,     Sandblast  Action  in,  70 
„     Shadow  of,  352 
„     Shape  of,  See  Shape  of  Arc 
„     Smell  of,  28 
„     Sounds  emitted  by,  39,  46,  69,  277, 

279,  300 

„    Source  of  Heat  in,  393 
„     Sources  of  Light  in,  314 
Arcs,  Sizes  of,  with  S.  &  C.  Carbons  com- 
pared, 6,  15,  16,  419 

Arc,  Stability  of,  Conditions  for,  62, 243, 248 
,,     Starting  of  Heat  and  Light  in,  31 
„     Striking,  See  Striking  the  Arc 
„     in  Sulphuric  Acid,  31 
„     Temperature  of,  38,  65,  68,  354 
„     Unilateral  Conductivity  in,  71 
„     in  Vacuo,  25,  32,  47 
„     Various  Layers  in,  348,  354,  392 
„     Vapour  Film  in,  See  Vapour  Film 
„     with  Water  Electrode,  33 
Area  of  Crater,  Apparent,  316,  445 
„  „        and  Candle  Power,  316, 337 

„  „         and  Candle  Power,  Curves 

for,  320,  321,  322 
and  Cur.,  39, 158,  292,  364, 

394,  396 

„  „        Definition  of,  144 

„  „        and  Hissing  Points,  297 

and  1, 14,  151,  396 
„  „         and  I,  Curves  for,  155 

„  „         Measurement  of,  39,  151 

„  „         Obscured  by  Neg.  Carbon, 

315,  322,  339 

,,  „        and  P.D.,  153 

,,  „         and  Tip  of  Pos.  Carbon  for 

Hissing,  61,  294 
„     of  Disc,  Apparent,  445 
„     of  Volatilising  Surface  of  Crater,  396 
Arons,  49,  81,  95,  96 
Ayrton,  W.  E.,  36,  45,  61,  75,  95,  97,  126, 

207,  281,  326,  333,  364 
Ayrton  &  Perry,  40,  95,  124 


Back  E.M.F.  of  Arc,  138,  391,  393, 407,  440 
„  „          „     Discussion  on,  225, 398, 

439 

„  „  „     Experimenters  on   34, 

36,  37,  39,  40,  42,  44, 

46,47,50,52,61,64, 

72,  81,  84,  88,  90,  91 

„  „  „     Precautions  in  Testing 

for,  416 

,,  „  „     and  Vapour  Film,  398 

„  „  „     Varying    with    Added 

Alt.  Cur.,  416 
Basquin,  Crew  and,  459 
Battery,  Davy's  Royal  Institution,  26 
Becquerel,  31,  94,  95 
Blondel,  62,  67,  88,  90,  96,  248,  293,  329, 

347,  364,  375,  377,  380,  386,  459 
Blowing  on  Arc,  Effect  of,  65,  305 
Blowpipe,  Electric,  33 
Bright  Spot  in  Crater,  69 

„       Spots  on  Carbons,  4 
Brilliancy  of  Crater,  64,  66,  67,  83,  84,  314, 

321,  346 
„  „         Constancy     of,     64, 

321,  346 
„  ,,         Diminution   of   with 

Hissing,  68,  292 
„  „         Uniformity  of,   314 

321,  347 
Brown,  459 
Burch,  Expts.  on  Candle  Flame,  351 

Candle  Flame  Expts.,  350,  456 
„      Jablochkoff,  35 

„       Power  and  Area  of  Crater,  316,  337 
„  „  „  „          Curves 

for,  320,  321 
„  „       and  Cur.,  366 

„       and  I,  328,  330,  342 
„  „       and  I,  Curves  for,  329,  330 

„          „       Mean    Spherical,   Definition 

of,  451 

„  „          „  „     and  Rousseau's 

Figures,  344, 452 

„  „          „  „    and  Total  Light, 

330,  344,  450 
„  „      Method  of  Measuring,  326 

„      Polar  Curves  for,  320, 321, 455 
„       Shadow  Expts.,  456 
„  „        See  also  Light,  Total 

Cantor  Lectures  (Thompson),  24,  458 
Carbon,    Cored    Negative,    See    Negative 

Carbon 
„  „         Positive,      See      Positive 

Carbon 

„        Dioxide.  Arc  in,  38,  65,  83,  87 
„  „          Blown  at  Crater,  305, 30 


INDEX  TO  CONTENTS. 


463 


Carbon,   Dioxide,  Compressed,    Temp,   of 

Crater  in,  83 

„  „          Vacuum  Discharge  in,  37 

„        Exploring,  See  Exploring  Carbon 
„       Mist,  See  Mist 
,,        Monoxide,  Arc  in,  65 
„        Negative,  See  Negative  Carbon 
„        Normal,  Definition  of,  104 
„        Particles  in  Arc,  84,  349 
,,       P.D., Negative, /S'ecNegative  Carbon 
„        P.D.,  Positive,  See  Positive  Carbon 

P.Ds.,  Sum  of,  and  Cur.,  226 
„  „  „        Cur.  and  I,  Equa- 

tion for,  225, 231 
„       Plates,   P.D.    between    Hot   and 

Cold,  57 

,,       Positive,  See  Positive  Carbon 
„       Power,  Negative,     See     Negative 

Carbon  Power 

„  ,,         Positive,  See  Positive  Car- 

bon Power 

„       Softening  of,  28,  62,  347 
„        Soft,  Proportion  of  in  Crater,  144 
„       Solid  Negative,  See  Negative  Car- 
bon, Solid 

„  „     Positive,  See  Pos.Carbon,  Solid 

Carbons  and  Arc,  See  Arc  and  Carbons 
„       Appearance  of,  4,  sqq. 
„        Bright  Balls  on,  4 
„       Change  of  Shape  of,  with  Sudden 

Change  of  Cur.,  14,  106 
„        Cold,  Striking  Arc  with,  111 
,,        Composition  of,  and  Light,  386 
„       Consumption  of,  30,  32,  386 
Cooled,  P.D.  with,  47,  53,  86 
„        Cored,  See  Cored  Carbons 
„       Cores  in,  Effect  of,  See  Cores 
,,        Diameters  of,  See  Diameters 
„        Hot,  Striking  Arc  with,  111 
„       Lengths  of  Tips  of,  7,  295,  395 
„       Light  of,  2,  315,  345,  376 
„        Normal,  Definition  of,  104 
„       Outer  Crust  on,  4 
„        Parallel,  Arc  with,  36 
„       Particles  Shot  out  from,  4,  28,  30, 

32,  84,  349 

„       P.D.  between,  See  P.D. 
„       Shapes  of,  8, 106,  293,  296,323,  393 
„  „        with  Hissing  Arcs,  294 

„  „         Change  of,  with  Sudden 

ChaQge  of  Cur.,  14, 106 
„  „         Explanation    of    Varia- 

tions in,  13, 14, 106, 393 
„      Sizes  of  Arcs  with  C.  and  S.  com- 
pared, 6,  15,  16,  419 
„       Sizes  of,  See  Diameter 
,,       Slow-burning,  Need  of,  384 


Carbons,  Solid,  See  Solid  Carbons 

„        Sprinkled  with  Metallic  Salts,  56 
„        Steeped  in  Metallic  Salts,  31 
„        Temperatures   of,  in  Arc,    Differ- 
ence of,  29,  32,  38,  45,  65 
„        Vapour,  See  Vapour 
„        Volatilisation  of,  at  Crater,  28,  64, 

68,  84,  346,  347,  355,  392,  393 
Carhart,  334 
Casselmann,  31,  95 
Cause  of  Hissing,  299,  305,  308 
Charcoal  Terminals,  20,  23 
Chlorine,  Arc  in,  65 

Cold  Carbons,Effectof  Striking  Arc  with,lll 
Colour  of  Arc  Light,  356 

„  „         Experiments  on,  358 

„         Crater  Light,  Hissing  Arc,   68, 

277,  293,  300 

Colours  of  Arc  and  Carbons,  4 
Commercial  Arc  Lamps,  383 
Compressed  Gases,  Arc  in,  83 
Conductivity  of  Arc,  57,  71,  392 
Constancy  of  Brilliancy  of  Crater,  64,321,346 
Consumption  of  Electrodes,  30,  32,  386 
Contact  Resistance  between  Arc  and  Car- 
bon, 43,  50,  51 

Convex  Crater  with  Long  Arcs,  60,  394 
Cooling  Carbons  and  Arc,  47,  53,  86 
Corbino  and  Liga,  459 
Cored  Carbons,  Cross-section  of  Arc  with, 

6,  16,  419 

„  „          of    Arc    with, 

Slowness    of 

Changes    in, 

406,  428 

„  „  „  of  Mist  with,  7, 

15,16,419 

„  „  „          of  Vapour  Film 

with,  421 

^X  and  Cur.  with,  79,  432 
5A 

„         Frequency     with, 

81,407,437 
Zwith,  79,  434 

„  „        Light  of  and  Cur.,  364 

„  .,  „     Efficiency  and  I  with, 

381 

„    and  I  with,  328,  334 
„  „  „     of,  and  of  Solid,  Com- 

pared, 377,  386 
„  „         Max.  Light  Efficiency  with, 

and  I  381 

„  „        Neg.  Carbon,P.D.  with,  237 

„  „        P.D.  between,  with  Third 

Carbon  in  Arc,  235 

„  „        when  P.D.  Independent  of 

Cur.  with,  141 


464 


INDEX  TO  CONTENTS. 


Cored  Corbons,  Pos.  Carbon,  P.D.  with,  235 
„         and  Solid,  Appearance  of 
Arc  with,  Compared,  6, 
15,  419 

„  and  Solid,  Hissing  Points 
with,  Compared,  133, 
291,  417,  424 

|f  „         and  Solid,  P.D.  and  Cur. 

Curves  with,  Compared, 
132,  417 

„         and  Solid,  P.D.  for  Hissing 

Arcs  with.  Compared,291 

and     Solid,    P.D.    and    I 

Curves  with,  Compared, 

142 

„        Vapour    P.D.    with,    236, 

238 

,,      Negative  Carbon,  See  Negative  Car- 
bon, Cored 
„      Positive  Carbon,  See  Positive  Carbon 

Cored.     See  also  Core  and  Cores 
Core,  Light  from,  and  from  Solid  Carbon, 

377,  386 

„    Mist  from,  421 
„    in  Neg.  Carbon,  Crater  caused  by,  16, 

238 

Core  in  Positive  Carbon- 
Effect  of  on  Hissing  Point,  133,  291, 

417 

„  „        Hissing  Point,Cause  of,  424 

Largest  Silent   Cur.,   133, 

291,  417 
„  „         P.D.-Cur.  Curves,  26,  sqq., 

417,  sqq. 
„  „         P.D.-Cur.  Curves,  Cause  of, 

143,  417,  422 
P.D.-Z  Curves,  131, 139 
„        P.D.  on  Striking  Arc,  103, 

107 
„  „        P.D.  with  Sudden  Change 

of  Cur.,  115 

„    Min.  P.D.  with,  for  Given  I,  131,  135 
„     Shape  of  Arc  with,  6,  7,  8,  81 
„     Size  of,  and  Light,  377 

See  aho  Cores  and  Cored  Carbons 
Cores,  Composition  of,  422 

„       Effect  of  on  Change  of  Cross-section 
of  Mist,  425 

„  „  ,,          Cross-section 

of     Vapour 
Film,  425 
„  „          Cross-section  of  Mist,  6, 

15,  16,  419 

„  ,,         Cross-section  of  Vapour 

Film,  421 

1^,78,81,418,424,431 

oA 


Cores,  Effect  of  on-        427 
oA 


„          P.D.  between  Carbons, 

131,  139,  417 
P.D.  between  Carbons, 
Cause  of,  133,  143,  422 
Res.  of  Arc,  78,  417,  429 
„     Mist,  418,  429 
„     Vapour  Film,  421, 

429 

Size  of  Arc,  7,  15,16,419 
Core,  Purple^  of  Arc,  2,  5,  6,  7,  57,  356,  392 
Core,  Vapour  from,  421 

See  also  Cored  Carbons 
Crater,  Area  of,  See  Area  of  Crater, 

„       Volatilising  Surface  of,  396, 

399 

„      Air  blown  at,  303,  305,  307 
,,      Air  touching,  effect  of,  299 
„      Black  S  pots  on,  with  Hissing,  68,  292 
„      Bright  Spot  in,  69 

Brilliancy  of,  64,  66,  67,  83;  84,  314, 

321,  346 
„  „  Diminution    of,    with 

Hissing,  68,  292 

„      Carbon  Dioxide  blown  at,  305,  307 
„      Co  a  vex  with  Long  Arcs,  60,  394 
„      with  Cored  Neg.  Carbon,  11,  16,  238 
„      Dark  Bands  on,  69,  277,  292 
„      Darkening  of,  with  Hissing,  68,  292, 

299,  301 

„      Depth,  See  Depth  of  Crater 
„      Diameter  of,  See  Diameter  of  Crater 
„      in  Exploring  Carbon,  71,  211 
„      First  Observed  in  Pos.  Carbon,  28 
Formation  of,  393 
of  Hissing  Arc,  39,  68,  292,  294,  297, 
299 

and    End    of    Pos. 
Carbon,  60,  294,297 
,,      Hydrogen  blown  at,  306,  307 
„      Light,  314,  335 

Absorption  of,  by  Arc,  349,  357 
„      and  I,  360 
Angles  Measuring,  324 
Area  Proportional  to,  337 
Colour  of,  with  Hissing  Arcs, 

68,  277,  293,  300 
Constant  Intrinsic  Brilliancy 
of,  64,  66,  67,  83,  84,  314, 

321,  346 

Cut  off  by  Neg.  Carbon,  315, 

322,  339 

Emitted  by  and  Received  from, 
348 


INDEX  TO  CONTENTS. 


465 


Crater  Light,  and  I,  Curves  for,  from  Dia- 
grams, 335,  342,  362 
.,          „     Uniform  Distribution  of,  314, 

321,  347 

„      in  Negative  Carbon,  11, 16, 238 
Nitrogen  blown  at,  305,  307 
Oxygen  blown  at,  305,  307 
Pitting  of,  with  Hissing,  39,  292,  299 
Plasticity  of,  61 

Proportion  of  Soft  Carbon  in,  144 
Ratios,  Calculation  of,  154 
,,      Definition  of,  145 
.,      Hard,  and  P.D.,  157,  158 
'.,      and  Size  of  Pos.  Carbon,  164 
„  '    Soft,  and  I,  146,  156 
„      Values  of,  156 
Size  of,  See  Area  of  Crater 
Surface,  becoming  Graphite,  68 
„         Nature  of,  and  P.D.,  133, 

422 
,,      Temperature  of,  See  Temperature 

of  Crater 

,,      Vapour  Film,  and  Volatilising  Sur- 
face, 396,  399 

,,      Volatilisation.  See  Volatilisation 
Cravath,  63,  96,  307 ' 
Crew  and  Basquin,  459 
Cross-section  of  Arc,  Diagrams  for  Measur- 
ing, 401 
„  „       Effect  of  Cores  on,  6, 

15,  419 

„       and  I,  8,  395 
„  „       and  Res.,  398 

„  ,,       and  Volume,  395 

„          of  Carbons,  See  Diameter 
of  Mist,  16,  401,  419,  425 
„          of  Mist,  effect  of  Cores  on,  6, 

15,  419 
„          of  Mist,  effect  of   Cores  on 

Change  of,  425 
of  Mist  and  Cur.,  402,  420 
of  Vapour  Film,  404,  421 
„          of    Vapour   Film,    effect    of 

Cores  on.  421 
„          of    Vapour'  Film,   effect    of 

Cores  on  Change  of,  425 
„          of  Vapour  Film,  and  Cur.,  421 
„          of  Vapour  Film,  and  I,  397 
Crookes,  64 

Cross  and  Shepard,  46,  95,  166,  198,  279 
Crucible  for  Enclosing  Arc,  301 
Cruickshanks,  21 

Current,  Added  Alt.,  Affecting  Arc,  50,  55, 

78,  406 

,,  „  „  »  Tests  for, 

414,  416 

„     Back  E.M.F.,  416 


Current,  Added  Alt.,  Measurement  of  Res. 
of  Arc  with,  49,  50, 
54,  71,  75,  406 
„       and  Area  of  Crater,  See  Area  of 

Crater 

,,       and  Candle  Power,  364,  sqq. 
„       Carbon    P.Ds.    and   I,    Equation 

for,  225,  231 

,,       Cessation   of,    Duration   of    Arc 
after,  35,  39,  64,  84,  89,  91 

„       Constant, and5-!,  81 

oA 

„  ,,         Impossibility  of  Keep- 

ing, 244 
„       and  Cross-section  of    Mist,    402, 

420 
„  ,,  „         of  Mist,  Curves 

for,  420 
„  ,,  „         of  Vapour  Film, 

421 

„       and  Depth  of  Crater,  160 
„       and    Diameter    of     Crater,     See 

Diameter 

,,       Duration  of  Arc  after  Stopping, 
35,  39,  64,  84,  89,  91 

„      and  g,  79, 432 

and  -— e,  Curves  for,  432 
5A 

and  — -*,  Curves  for,  430 

8A 
„      and  E.M.F.  Fixed,  Max.   I  with, 

254 
„        Min.  Res.  with, 

256 
„       E.M.F.,  /,  and  Series  Resistance, 

Equation  for,  253 
„       and  External  Resistance,  252 
„       Increase  of,  at  Hissing,  278,  289 
„       and  I,  167 
„  „      Const,   Time    Change    of 

P.D.  with,  97,  106,  404 
„      Curves  for,  169 
„      at  Hissing  Point,  262,  282 
„       Largest  Silent,  133,  278  to  299 
,,       and  Light,  See  Light 
„       Minimum,  with  given  E.M.F.,  and 

,,  „  „      given  E.M.F.,  and 

Series  Res.,  253 
„       and  Neg.  Carbon  P.D.  217 

„       P.D.,  Curves  for, 

218 
„       P.D.,    Equation 

for,  224 
„       Power,  224 


466 


INDEX  TO  CONTENTS. 


Current,  Oscillation  of,  with  Hissing,  54, 

81,  309 
,.  „          of  Air,  with  Hissing, 

309 

„       and  P.D.,  See  P.D.  and  Current 
„       and  Pos.  Carbon,  P.D.,  214 
„  „  „         P.D,      Curves 

for,  215 

„  „  „         P.D.,  Equation 

for,  222,  286, 
400 

Power,  220 
„  „  ,,         Power,  Curves 

for,  221 

„      and  Power,  See  Power 
„       and  Resistance,  See  Resistance 
„      and  Shape  of  Arc,  6,  7,  8,  293 
„  „  of  Neg.  Carbon,  8,  10, 

11,294,323,335,394 
„  „  of    Pos.    Carbon,    13, 

294,  393 
„       Small,  Difficulty  of   Maintaining 

Arc  with,  176,  249 
„  „      Large  E.M.F.  needed  for, 

249 

„       Smallest  Hissing,  278,  288 
„       Sudden  Change  of,  and  Shape  of 
Carbons,  14, 
106 

„  „  „       Time     Change 

of  P.D.  with, 
112,  404,  435 

„      and  Sum  of  Carbon  P.Ds.,  225 
„      Time  Change  of,  with  Const.  P.D., 

171 
„  „  „       of,  and  of  P.D.  and 

Res.,  404,  407 
„      and  Vapour  P.D.,  232 
Curves  for   Area  of   Crater  and    Candle 
Power,  320,  321 
„  „  ,,       and  Cur.  159 

and  I,  155 

„  „  „       and  P.D.,  153 

„        Candle  Power  and  Cur.,  366 

I,  329,  330 
n  „  „          Polar,     320, 

321 
,,        Carbon  P.Ds.,  Sum  of,  and  Cur. 

226 

„         Crater  Light  and  I,  from  Dia- 
grams, 343,  363 

„         Cross-section  of  Mist  and  Cur.,420 
„         Current  and  I,  169 

~  and  Cur.,  79,  434 
oA 

-c  and  Cur.,  432 


Curves  f or |Xf  and  Cur.,  430 
5A 

"      5A and  Frequency,  4125  438 

—  and  I,  436 
oA 

„        |Y  and  P.D.,  80 

„       Hard  Crater  Ratio  and  P.D.,  157 
„       for  Light  and  Area  of  Crater,  320, 

321,  322 
and  Cur.,  367 

„  „         Efficiency  and  Cur.,  385 

„    1, 381, 382 

and  I,  330,  333,  334,  343, 

363 
„      for  Neg.  Carbon, P.D.  and  Cur., 218 

,,    2,219 
„  „  „     Power  and  Cur., 

224 

„       for  P.D.  and  Cur.,  101,  120,  128, 

129,130,132, 

177,187,242 

280,  423 

„  „  „     Enclosed     Arc, 

304 

„  „  „     and  Res.  of  Sta- 

bility, 62,  242 
„    and  Z,  136,  139,  140,  142, 

144,  163 

„       Polar,  for  Candle  Power,  455 
„  „  „         Power  and  Area 

of  Crater,  320, 
321 
„       for  Pos.  Carbon,  P.D.  and  Cur.,  215 

„       2,216 
„  „  „      Power  and   Cur., 

221 

„  „  „      Power  and  I,  220 

„       for  Power  and  Cur.,  182, 196,  200, 

403 

„       for  Power  and  1, 180, 194, 199,  373 
„       for  Res.  and  1, 164,  165,  166 
„      for  Soft  Crater  Ratio  and  I,  156 
„       for  Time  Change  of  Cur.,  171 

„  P.D.,  103,  105, 
107,  109,  110, 
113,  114 

„  P.D.  with 
Change  of  Cur., 

435 

„     P.D.,  Cur.,  and 
Res.,  405, 408 
Cuthbertson,  24,  94 
Daniell,  30,  94 
Dark  Bands  on  Crater,  69,  277,  292 


INDEX  TO  CONTENTS. 


467 


Darkening  of  Crater  with  Hissing  Arc,  68, 

292,  299,  301 

Dark  Spaces  in  Arc,  5,  6,  7,  81 
Davy,  20,  25,  94 

Deflection  of  Arc  by  Magnet,  27,  33 
Definition  of  Area  of  Crater,  144 
„  Crater  Ratios,  145 

v— ,  Instantaneous  and  Steady, 


oA 


77 


Hissing  Point,  282 
Length  of  Arc,  99 
Lumen,  330 
Mean  Spherical  Candle  Power, 

451 
Negative  Carbon  P.D.,  212 

„  Power,  220 

Normal  Arc,  104 

„        Carbons,  104 
Positive  Carbon  P.D.,  212 

Power,  220 
Resistance  Lines,  243 
Vapour  P.O.,  212 
White  Spot,  210 
De  la  Rive,  31,  32,  95 
De  la  Rue  and  Miiller,  37,  95,  302 
Depth  of  Crater,  47,  138,  144 
and  Cur.,  160 
and  Diameter,  63 
and  I,  160,  393 
Measurement  of,  160 
and  P.D.,  159 
Description  of  ARC,  See  Appearance 
Dewar,  40,  95,  349 

Diagrams  of    Arc  and  Carbons,  3,   9,  10, 

12,  15,  16,  293.  295,  318,  319, 

324,  336,  340/365,  376,  379, 

418 

„          Curves  for  Crater  Light  and  I 

from,  335,  343,  363 
„         for  Measuring  Cross-section    of 

Arc,  401 
Diameter  of  Crater,  and  Cur.,  14,  39,  63, 

151 
Measurement  of,  39, 

151 

„  „          Observed  and  Calcu- 

lated, for   Different 
Currents,    154    See 
also  Area  of  Crater 
„  Positive  Carbon,  and  Crater 

Ratios,  164 
Diameters  of  Carbons,  Effect  of  on  P.D.,  161 


Diameters   of   Carbons  and  Hard   Crater 

Ratio,  154 
„  „  and  Largest    Silent 

Cur,,  281 
„  „  and  Light  Efficiency, 

374,  sqq. 

„  „  and     Light    Effici- 

ency, Precautions 
in  Measuring,  378 
Disc,  Apparent  Area  of,  445 

„     Rotating,  as  Electrode,  56 
Discharge  in  Vacuum  Distinguished  from 

Arc,  37,  44 
Disturbance  of  Arc  by  Exploring  Carbon, 

58,  210,  228 
Dubs,  57,  96 
Duddell,  411,  459 

„         and  Marchant,  309 
Duncan  Rowland  and  Todd,  66,  96, 188,  203 

—  with  Added  Alt.  Cur.  Change  of  Sign 

5  A  w  i  t  h      F  r  e  - 

quency,81,407, 

437    ' 

„  „  ,,         and  Const.  Direct 

Cur.,  81 

„  „  „         with  Cores  in  Car- 

bons,   78,    81, 
418,  424,  431 
and  Cur.,  79,  432 
,,         and      Frequency, 

81,  407,  437 
„  „  .,         and  I,  79,  434 

„        Neg.  Value  of,  54, 
75,  81,  407,  sqq. 

„  .,  „         Neg.  Value  of ,  for 

Normal  Arc,  S. 
Carbons,  402 

„  „  „         Normal  and  Non- 

normal   Values 
of,  427 
and  P.D.,  Curves 

for,  80 

„  ,,  „        and  Resistance  of 

Arc,  when  Equal, 
406,  410 
Sign  of,  427 

— ,  Definitions  of  Instantaneous  and  Steady, 
5A    77 

^  and  Cores  in  Carbons,  427 
oA 

„    and  Cur.,  Curves  for,  432 

„    Definition  of,  424 

-Xf  and  Cores  in  Carbons,  429 
oA 

„    and  Cur.,  Curves  for,  430 

„    Definition  of,  425 


468 


INDEX  TO  CONTENTS. 


Edlund,  33,  46,  95,  138,  166,  189,  281,  458 
Efficiency  of  Arc  Lamps,  383 

„         Light,  See  Light  Efficiency 
„         Power,  See  Power  Efficiency 
„         of  Sources  of  Light,  Comparing, 

388 

Electric  Blowpipe,  33 
„        Flame,  Davy,  24 
„       Spark,  See  Spark 
Electrode,  Carbon  Disc  as,  32 

„          Rotating  Disc  as,  56 
Electrodes  and  Arc,  See  Arc  and  Carbons 

Consumption  of,  30,  32,  386 
„          Matter  Shot  out  from,  4, 28,  30, 

32,  84,  349 
Metal,  28,  29,  30,  31,  32,  33,  35, 

50,56 
„          Qualities   needed  in,  for  Good 

Light,  30,  52 

Temp,  of,  29,  32.,  38,  45,  65 
„          Various,   Arc  between,  22,  24, 

28,  30,  31,  32,  35,  50,  56 
„          Water  as,  33 

Electrolytic  Theory  of  Arc,  30,  62,  66,  90 
E.M.F.,  Back,  Sec  Back  E.M.F. 

„        of  Generator,  Const.,  Arc  with,  241, 

sqq.,  265 

„  „  and  Cur.  Const.,  Min. 

Series     Res.,    and 
Max.  I  with,  254 

„  „  Cur.,   I,    and   Series 

Res.,  Equation  for, 
253 

„  „  Large,  required   for 

small    Cur.    Arcs, 
249 

„  „  and  I   Const.,  Max. 

Res.  and  Min.  Cur. 
with,  246,  255 

„  „  Minimum,  for  Main- 

taining Arc,  251 

,,  „  and  Power  Efficiency 

ofArc,261,265,270 

M  „  and  Series  Res.  Const., 

Max.  I  with,  253 

„  „  and       Series       Res. 

Const.,  Min.   Cur. 
with,  253 
,,  „  and  Smallest  Hissing 

Cur.,  288 
»  „  and  Stability  of  Arc, 

248 
Enclosed  Arcs,  25,  30,  32,  37,  44,  47,  65, 

67,  72,  83,  86,  301 
„  Hissing  Absent  with,  301 

„  Hydrogen  not  causing  His- 

sing in,  307 


Enclosed  Arcs,  P.D.  and  Current  Curves 

for,  304 
Equations  for  Carbon  P.Ds..  Cur.  and  1, 225, 

231 
„  Cur.  and  I  at  Hissing  Points, 

262,  282 
„  Cur.    and    P.D.    at    Hissing 

Points,  284 
5V   5VC       ,  5VS  nnc 
»  *A '  WT  and  TT>  425 

OA.     OA  OA. 

„  ;— ,   Res.,     Cur.     and     Back 

5A      E.M.F.,  406 
„  E.M.F.,  I,  Cur.  and  Series  Res., 

253 
,.  E.M.F.,  P.D.,  Cur.  and  Series 

Resis.,  253 

Fall  of  ^  P.D.    with  Hissing, 

Increa'se  of  Cur.  and  r,  289 

„  Fall  of  P.D.  with  Hissing,  and 

I,  288 

„  N  eg. Carbon  P.D.  and  Cur.,  224 

„  „  Power  &|Cur.,  224 

„  P.D.,  Back  E.M.F.,  Cur.  and 

Res.,  406,  416 
„       and  Cur.,  191,  204 
„  „       Cur.  and  I,  50,  51,  64, 

66,  67,  184, 186,  195, 
200,   202,   203,  204, 
225,  231,  253 

,,  „       Cur.  and  I,  Meaning  of 

Terms  in,  232 
„       Cur.  and  £,  with  Third 

Carbon  in  Arc,  230 
„  „       Cur.  and  Res.,  74 

,,       and  1, 40, 41, 49, 50, 55, 

67,  192 

„  „       and    I,    with    Hissing 

Arcs,  284 
„  „       and  I,  at  Hissing  Points, 

282 

„  Pos.  Carbon  P.Ds.,  Cur.  and 

I,  222, 286, 400 

,,  „          „       Power  and  Cur., 

222 
„       Power,  Cur.  and 

J,222 

„  „          „       Power  and  Z,  222 

Power  and  Cur.,  183, 191, 195, 

200,  204 
„      Cur.  and  1, 42, 183, 186, 

188,  195,  200,  202 
„      and  1, 181, 193,198,200 
„  „      Efficiency,  Cur.,  I  and 

Res.,  259 

„  Resistance,  Cur.  and  1, 41, 195, 

201,  203 


INDEX  TO  CONTENTS. 


469 


Equations  for  Resistance  and  I,  34,  42,  46, 

166, 189 

„  „         and  I  with  Hissing 

Arcs,  47, 166,  281 

„  „     of  Mist  and  Cur.,  403 

.     of  Mist,    Cur.   and   I, 

403 
„  „     of  Vapour  Film,  Cur. 

and  I,  400 
„  Resistances  of  Vapour   Film 

and  Mist,  Cur.  and  I,  403 
Expansion  of  Gas  on  striking  Arc,  38,  45, 

302 

Exploring  Carbon  in  Arc,   P.D.  between 

Carbons    with,     S.S., 

229,C.S.andC.C.,235 

„  „       Attraction  of  Arc  by,  211 

,,  „       Bare,  Objections  to,  213 

„  „       Cratering  of,  71,  211 

,,  ,,       Disturbance  of  Arc  by, 

58,  210,  228 
„       First  used,  53, 
„  „       Method  of  Experiment- 

ing with,  208 

„  „       Pointing  of,  57,  211 

,,  „       Repulsion  of  Arc  by,  58, 

210 
,,  ,,        Tip  of   Converted  into 

Graphite,  71 

External  Resistance,  See  Resistance  in  Series 
with  Arc 

Fall  of  P.D.  when  Blowing  Air  at  Crater, 

305,  307 

„  „  „          Hydrogen     at 

Crater,  306 

„  „  ,,          Oxygen      at 

Crater,  305, 
307 
at  Hissing,  39,  63,  278 

Cause  of,  308 
„  and  I,  288 

,,       Potential  through  Arc,  Rate  of,  59 
.,  ,,         at    Neg.  Carbon,    See 

Negative  Carbon  P.D.' 
,,  „         at   Pos.    Carbon,    See 

Positive  Carbon  P.D. 
Faraday's  Law  of  Electrolysis  applied  to 

Arc,  30 

Feussner,  50,  96 
Fitzgerald,  Wilson  and,  83,  96 
Flame  of  Arc,  observed  by  Davy,  24,  25 

„     Green,  5,  6,  57,  60,  68,  392 
„  „     Formation  of,  392 

„  „     High  Resistance  of,  392 

„         Candle  and  Gas,  Expts.  on,  350, 
4,56 


Fleming,  70,  93,  96,  459 

Fourcroy,  Vauquelin  and  Thenard,  22,  94 

Freedman,  72,  96 

Frequency  of  Added  Alt.  Cur.  and    5— , 

81,  407,  437  5A 

„  Added  Alt.  Cur.  and  Sign  of 

g,  81,  407,  437 

Frith,  71,  96 

Frith  and  Rodgers,  76, 96,  309,406,  411,  418 

Frolich,  41,  95,  138,  191 

Gas  Flames,  Expts.  on,  456 
Gases,  Arc  in  Various,  30,  45,  65,  83 
Gassiot,  29,  94 

Generator,  E.M.F.  of,  See  E.M.F. 
Gilbert,  22,  94 
Granquist,  91,  96 

Graphical  Study  of  Conditions  of  Arc,  241 
Graphite,  Surface  of  Crater  becoming,  68 
„         Tip   of   Exploring  Carbon  con- 
verted into,  71 
Gray,  Wilson  and,  459 
Green  Flame  of  Arc,  5,  6,  57,  60,  68,  392 
Grove,  30,  33,  94,  95 
Guillaume,  84,  96,  459 

Hard  Crater  Ratio,  Calculation  of,  154 
„  „       Definition  of,  145 

„       and  P.D.,  157 
,,  „      and  Sizes  of  Carbons, 

164 

Hare,  28,  94 

Heat  of  Arc,  Source  of,  393 
„     in  Arc,  Starting  of,  31 
Heating  Pos.  Carbon,  Effect  of,  47,  53 
Heat  Radiation  Compared  with  Light  in 

Arc,  369 

Herzfeld,  84,  96,  349 
Hess,  459 

Hissing,  Absent  with  Enclosed  Arcs,  301 
,,       Arcs,  277,  sqq. 

„     Appearance  of.  68,277,292,300 

„          „  „  Crater  of,  39, 

68,  292,  299 

„     Colour  of,  68,  277,  293,  300 
„  „     Cur.  Density  and  End  of  POP. 

Carbon  with,  60 
„     Crater  of,  39,  68,  292,  294, 

297,  299 
„  „     Crater  Area  and  Tip  of  Pos. 

Carbon  with,  61,  294 
„  „     Crater  of,  Darkening  of,  68, 

292,  299,  301 

„     Crater  of,  Pitting  of,  39,  292, 
299 


470 


INDEX  TO  CONTENTS. 


Hissing  Arcs,  Diminution  of  Res.  with,  28? 

„  ,,     Experimenters  on,  28,  31,  39 

40,  46,  53,  56,  60,  63,  68 

86,  279,  281,  286,  294,  307 

309 

„     Increase  of  Cur.  Avith,  278, 288 
„  „     Laws  of,  and  Shape  of  Pos. 

Carbon,  298 

„  „     Light  from,  68,  277,  293,  300 

„     Mushroom  with,   11,  28,  86, 

293,  294,  300 

„  „     Neg.  Carbon  P.D.  with,  287 

„          „     Normal,  Laws  of,  279 
„          „  „       andNon-normal,285, 

299 
„  „     Oscillations  of  Cur.  with,  54, 

81,  309 

„     Oscillatory  Air  Cur.  with,  309 
„  „     P.D.   Constant   for  given    /, 

279,  282,  288 

„     P.D.  with  C.  Pos.  Carbon,  291 
„  „  „         C.  and  S.  Carbons 

compared,  291 

„     P.D.,  Fall  of,  with,  39, 63, 278, 
308 

and  I,  288 

,,  „          „  „         at  Pos.  Car- 

bon, 61,  286 

„  „     P.D.  and  I  with,  284 

„  „     Eesistance  and  I  with, 46, 166, 

281 

„          „    Shape  of,  293 
„          „  „          Carbons  with,  294, 

Caused  by  Air,  299,  305,  307 
„  „          Hydrogen,  306 

:>  >,          Hydrogen,    Not    with 

Enclosed  Arcs,  307 
„     ^    Oxygen,  305,  307 
„        Diminution  of  Brilliancy  of  Crater 

with,  68,  292 

and  Length  of  Arc,  279,  283 
„        with  Non-normal  Arcs,  285,  299 

Point,  Definition  of,  282 
»  ;,       Difference  of  with  C.  and  S. 

Carbons,   133,    291,   417 
424 

„       Pointp,  and  Area  of  Crater,  297 
„  „       Cur.  and  I  at,  262,  282 

P.D.  at,  282 
„       P.D.  and  I  at,  282 
„  „       and  Power  Efficiency,  261 

„       and   Silent   Arc,   Real    Difference 

between,  297 

„       Smallest  Current  with,  278,  288 
„      Sound,  39,  46,  69,  277,  300 
»  „      Cause  of,  308 

„      on  Striking  the  Arc,  301 


Hissing,  Unstable  Region  of,  133, 278,  281, 

History  of  the  Arc,  19,  sqq. 
Horizontal  Arc,  Shape  of,  26,  36 
Hot  Carbons,  Starting  Arc  with,  111 
Humming  Arc,  69,  277,  292,  300 
"  Hump  "  on  P.D.  Time  Curve,  107 
Hydrocarbon  Gas,  Arc  in,  65 
Hydrogen,  Arc  in,  30,  38,  45,  65,  83 

„          Blown  at  Crater,  Effect  of,  306, 
307 

„          Compressed,    Temperature     of 
Crater  in,  83 

„          Hissing  Caused  by,  306 

„          and     Hissing     with     Enclosed 
Arcs,  307 

„          Vacuum  Discharge  in,  37 
Hyperbola,  P.D.  and  Cur.  Curve  a,  186 

Idle  Carbon,  See  Exploring  Carbon 
Increase  of  Cur.  at  Hissing,  133,  278,  288 
Instability,  Region  of,  133,  278,  281,  289 

Instantaneous     — ,   Definition  of,  77 
Intensity  of  Source  of  Light,  How  judged, 

Intrinsic  Brilliancy  of  Crater,  64,  66,  67, 

83,  84,  314,  321,  347 
Inverted  Arc,  47,  81 

Jablochkoff  Candle,  35 
Janet,  459 
Jarvis  Smith,  459 

Lamp,  Arc,  Hand  Regulated,  98 
Lamps,  Arc,  Commercial,  383 

„         „     in  Series,  387 
Largest  Silent  Cur.,  133,  278,  288 

?>  „         Effect  of  Cores  on,  133, 

291,  417 
>,  „         Effect     of     Cores    on, 

Reasons  for,  424 

»  „         Effect  of  Sizes  of  Car- 

bons on,  281 
Le  Chatelier,  459 
Lecher,  52,  96,  207,  211 
Length  of  Arc — 

and  Absorption  of  Crater  Light,  360 
„     Appearance,  18 
„     Are*  of  Volatilisation,  397 
„     Candle  Power,  328,  330,  342 
»  „  Curves   for,    329, 

330 

„     Crater  Area,  14,  151,  396 
»  „         „      Curves  for,  155 

„      Depth,  160, 393 
»          „      Diameter,  See  Area,  above 


INDEX  TO  CONTENTS. 


471 


Length  of  Arc — 

„  and  Crater  Light,  from  Diagrams,  335, 

342 
„     „  „      Light,  from  Diagrams, with 

Absorption,  362 
„     „     Cross-section,  8,  395 
„     „  „  of  Vapour  Film,  397 

„     „     Cur.,  167 

„     „         „     and  Carbon  P.Ds.,  225,  231 
„     „         „     Curves  for,  169 
„     „         „     at  Hissing  Points,  262,  282 
,,     „         „     and  P.D.,  See  P.D. 
„     „         ,,     and  Power,  See  Power 
„  Definition  of,  99 

„  and  |Y,  79,  434 

0A 

„     „       „     Curves  for,  436 
„     „     E.M.F.,    Cur.,    and   Series  Res., 

Equation  for,  253 
„     „     E.M.F.  Fixed,  Max.  Series   Res. 

and  Min.  Cur.  with,  246,  255 
„     „     External  Res.,  245,  252,  255 
„     „     Fall  of  P.D.  at  Hissing,  288 
„  Fixed,  Const.  P.D.  for,  with  Hissing 

279,  282,  288 
„  Fixed,  Max.  Power    Efficiency  with, 

265,  270 

„  and  Hissing,  279,  283,  290 
„  Impossibility  of  Keeping  Constant,  243 
„  and  Light,  322,  332,  342,  345,  356 
„     „         „       Curves  for,  329,  330,  333, 

334,  343,  363 

„     „         „       Efficiency,  380 
„     „        „      Total,  330 
, ,     „         „          „     from  Diagrams,  342 
„     „         „  „     from  Diagrams,  with 

Absorption,  362 
„  Maximum    with    given    E.M.F.    and 

Cur.,  254 
„  Maximum   with    given    E.M.F.,    and 

Series  Res.,  253 

„  Maximum  with  given  P.D.,  167 
„  and  Max.  Light  Efficiency,  380 
„  Negative,  137 

„  and  Neg.  Carbon  P.D.,  218,  237 
„     „  „  Power,  224 

„     „     P.D.,  See  P.D.  and  I 
„     „     P.D.  and  Cur. ,  See  P.D.  Cur.  and  I 
„     „     Pos.  Carbon  P.D.,  216,  223,  236 
„     ,,  „          Power,  220 

„     „     Power,  178,  189,  195,  198 
„    „        „        Curves,  180, 194, 199, 373 
„     „         „         Efficiency,  260,  sqq. 
„     „        „         Equation    for,   181,   193, 

198,  200 

„    „    Resistance,  33,  41,  46,  131,  164, 
190 


Length  of  Arc— 

„  and  Resistance  of  Arc  Mist,  403 

„     „     Resistance,  Curves  for,  164,  165, 

166 
,.     „     Resistance,  Equation  for,  34,  42, 

46,  166,  189 
„     „     Resistance  with  Hissing,  46,  166 

281 

Resistance  of  Vapour  Film,  400 
Shape  of  Neg.  Carbon,  8,  10,  11, 

395 

Shape  of  Pos.  Carbon,  13,  398 
Soft  Crater  Ratio,  146,  156 

,3  „         Curves  for,  156 

„  Sum  of  Carbon  P.Ds.,  and  Cur.,  Equa- 
tion for,  225 

„  and  Time  Change  of  P.O.,  Ill,  114,434 
„     „     Vapour  P.D.,  232 
„  Zero,  P.D.  Decreasing  with  Increasing 

Cur.  with,  138 
„  Zero,  P.D.  Increasing  with  Increasing 

Cur.  with,  141 

Lengths  of  Tips  of  Carbons,  7,  295,  395 
Le  Roux,  39,  95 

Leyden  Jar,  Striking  Arc  with,  30 
Liga,  Corbino  and,  459 
Light,  Absorption  of,  by  Arc,  349,  sqq. 
„  „  by  Arc,  and  I,  360 

»  „  by  Candle       Flame, 

350,  456 
„       Apparatus  for  Measuring,  326,  327, 

331 

„       of  the  Arc,  313,  sqq. 
„  „         Colour  of,  356 

„  „  „         Expts.  on,  358 

„  „  „          with    Hissing, 

68,  277,  293, 
300 

Mist,  315,  357,  371 

„  „         Photographic  Power  of,  31 

„  „         Starting  of,  31 

„       of  Carbon  Tips,  2,  315,  345,  376 
,,       Comparison  of  Efficiency  of  Sources 

of,  388 

„       and  Composition  of  Carbons,  386 
„       from  Core  and  from  Solid  Carbon, 

377,  386 

„       of  Crater,  314,  335 
„  „       Angles  Measuring,  324 

„       and  Crater  Area,  Curves  for,  320. 

321,  322 
„       of    Crater,  Area    Proportional    to, 

337 
„  „       Brilliancy  of,  64    66,  67, 

83,  84,  314,  321,  346 
„  „       Colour  of,  with  Hissing, 

68,  277,  293,  300 


472 


INDEX  TO  CONTENTS. 


Light  of  Crater  and    /,    from    Diagrams, 

335,  342,  362 
„  „       and    I,     from   Diagrams, 

with  Absorption,  360 
„       Obstructed  by  Nesr.  Car- 
bon, 315,  322,  339 
„       Uniform  Distribution  of, 

314,  321,  348 
„      and  Cur.,  364 
„         „       „     Curves  for,  367 
„          „    Diameters  of  Carbons,  374 
„       Efficiency  of  Arc,  368,  sqq. 
„  „         Different   Sources,    Com- 

parison of,  388 

„  „         and  Cross-sections  of  Car- 

bons, 374 
and  Cur.,  384 

„      Curves  for,  385 
and  I,  380, 

and  I  Curves  for,  381,  382 
Maximum,  374 

and  I,  380 
Emitted    by    and     Received    from 

Crater,  348 
from  Ends  of  Carbons,  2,  315,  345, 

376 

of  Hissing  Arc,  68,  277,  293,  300 
Intensity  of  a  Source  of,  449 
and  Length  of  Arc,  322,  332,  342, 

345,  356 

„  ,,         Curves       for, 

330,333,334, 
343,  363 

Maximum  with  Const.  Cur.,  332 
from  Neg.  Carbon,  2,  31,  314,  345, 

376 
Percentage  of  Energy  Transformed 

into,  369 
Polar  Curves  for,  See   Polar  Light 

Curves 

and  Power  Expended  in  Arc,  370 
Qualities   of   Electrodes   for  Good, 

30,52 
Radiation  Compared  with  Heat'  in 

Arc,  369 
Refraction  of,  by  Arc,  353 

5)  „          Candle    and    Gas 

Flames,  456 

of  Short  Arc,  325,  327,  sqq. 
and  Sizes  of  Carbons.   See  Diameters 

of  Carbons 
and  Size  of  Core,  377 
Sources  of  in  Arc,  314 
Starting  of,  in  the  Arc,  31 
Total  and  Cur.,  364 
I,  330,  sqq. 
„          I,  from  Diagrams,  342 


Light,  Total,  and  I,  from  Diagrams,  with 

Absorption,  362 

„  „  Mean    Spherical    Candle 

Power,  330,  344,  450 
„       of  Vapour,  315 

Luggin,  54,  57,  96,  211,  281,  286,  294,  393 
Lumen,  Definition  of,  330 

Mackrell,  31,  95 

Magnet,  Deflection  of  Arc  by,  27,  33 

„        Noise  of  Arc  when  Extinguished 

by,  33 

„        Rotation  of  Arc  at  Pole  of,  29 
Marchant.  Duddell  and,  309 
Marks,  96,  386 
Mason,  29,  94 
Mather,  75,  352 
Matter  Shot  out  from  Electrodes,  4,  28, 

30,  32,  84,  349 
Matteucci,  32,  95 
Maximum  Length  of  Arc  with  fixed  E.M.F., 

and  Current  256 
„          Length  of  Arc  with  fixed  E.M.F. 

and  Series  Res.,  244,  253 
Length  of  Arc  withfixedP.D.,167 
Light  with  Const.  Cur.,  332 
„     Efficiency,  374 

and  I,  380,  381 
Power  Efficiency,  259j  sqq. 
Res.  in  Series  with  given  I  and 

E.M.F.,  246,  255 
Mean  Spherical  Candle  Power  and  Cur.,  328, 

368 
„  „       Candle    Power    and    Cur., 

Curves  for,  366 
„  „       Candle  Power,  Definition  of, 

451 

„    f        „       Candle  Power,  and  I,  328 
,,  „       Candle   Power,   and   Rous- 

seau's Figures,  344,  452 
.,  „       Candle    Power,    and    Total 

Light,  330,  344,  450 
Melting  of  Substances  by  Arc,  25 
Metals  Burnt  by  Electric  Spark,  22 
Metal  Electrode-,  28,  29,  30,  31,  32,  33,  35, 

50,56 

Metallic  Salts,  Arc  with,  31,  46,  56,  78 
Minimum    Current    with    I    and   E.M.F. 

fixed,  246,  255 
„  „         with  Series  Res.   and 

E.M.F.  fixed,  253 
„  „          with  Series  Res.  and 

I  fixed,  255 
„        E.M.F.   for  Maintaining    Given 

Arc,  251 

P.D.  for  Given  I  with  C.  Pos, 
Carbon,  131,  135 


INDEX  TO  CONTENTS. 


473 


Minimum  Point  in  Light-£  Curves,  328 

„         Resistance  in  Series  with   Arc, 

250,  251,  257,  274 
Mist,  Conducting  Power  of,  392 
„     from  Core,  421 

„     Cross-section  of,  16,  401,  419,  425 
„  „   and  Cur.,  402,  420 

„  and  I,  8,  395,  435 
„     Formation  of,  in  Arc,  392 
„     Light  of,  315,  357,  371 
„     Power  Wasted  in,  370,  403 
„     Resistance  of,  403 
„  „         with   C.  Carbons,  418, 

429 

„     Temperature  of,  355 
Mtiller,  De  la  Rue  and,  37,  95,  302 
Mushroom  on  Nee.  Carbon,  11,  28,  86, 293, 
294,  300 

Nakano,  369,  459 

Nebel,  47,  95,  141 

Neef,  31,  95 

Negative  Carbon  Cored,  Crater  in,  17, 238 
„  „  „        and   Cross    Sec- 

tion  of   Mist, 
419,  425 

„  „  „        and    Cross    Sec- 

tion of  Vapour 
Film,  421,  425 

„       and  ™  431 

oA 
„       and  Cur., 

432 

„  „  „  „       and  Fre- 

quency, 

„      andZ,437 
„       and  |J,427 

„  „        and  |J,  429 

„        and     Resistance 

of  Arc,  421 

„  „  „        Shape  of,  16 

Crater  in,  11,  16,  238 
„       Area  obscured  by, 
315,  322,  339 
„  „         Extra   Point    on,   with 

Short  Arcs,  11 
„  „        Flat,  Time  Variation  of 

P.D.  with,  108 
„  „        Length  of  Tip  of,  7 

„        Light  from,  2,  314,  345, 

376 

„  „        Light  cut  off  by,   315, 

322,  339 


Negative  Carbon,  Mushroom  on,  11, 28, 86, 

293,  294,  300 

„      „    P.D.,  Cause  of,  440 
„  „  with  C.  Carbons, 

237 

„  „  „     and  Cur.,  217 

„  „  „          „          Curves 

for,  218 

„  „  „  „         Equation 

for,  224 

„  „  „     Definition  of,  212 

„     and  Hissing,  287 
.      „  „     and  I,  219 

,,  „  „     with  S.    Carbons, 

217,  225 

„  „         Power  and  Cur.,  224 

„  „  „       Definition  of ,  220 

„       and  I,  224 

„  „         Shape  of,  and  Cur.,  8, 10, 

11,  294,  323, 

335,  394 

and  Z,  8,10,11, 

323,  393 

„  „  „        with     Short 

Hissing  Arc, 
294 

Shaping  of,  394 

„  „         Size  of,  and  Light,  379 

„         and  Time  Variation  of 

P.D.,  108 
White-hot  Tip  of,  2,  4, 

210,  314,  345,  376 
„        Length  of  Arc,  137 
„        Resistance,  54,  75,  78,  391,  400, 

406 

Niaude^,  39,  95,  279 
Nitrogen,  Arc  in,  45,  65 

„         Blown  at  Crater,  Effect  of,  305, 

307 
„        Compressed,    Temperature     of 

Crater  in,  83 
Non-normal  Arcs,  419,  421,  425,  426 

„      Hissing  with,  285,  299 
Normal  Arc,  Definition  of,  104 

„  Hissing,  Laws  of,  279 

Negative  Value  of  —   with, 

402  5A 

Normal  Carbons,  Definition  of,  104 

Original  Communications  on  the  Arc,  Lists 

of,  94,  458 
Oscillation  of   Air    Current  with  Hissing 

Arc,  309 

„  Electric  Current  with  Hiss- 

ing Arc,  54,  81,  309 
Oxygen,  Arc  in.'^S,  65,  83 


474 


INDEX  TO  CONTENTS. 


Oxygen  Blown  at  Crater,  Effect  of,  305,307 
„        Compressed,      Temperature      of 

Crater  in,  83 
„       Hissing  Caused  by,  305,  307 

Particles  of  Carbon  in  Arc,  84,  349 

„        Shot  out  from  Electrodes,  4,  28, 

30,  32,  84,  349 

Parallel  Carbons,  Arc  at  End  of,  36 
P.D.  between  Arc  and  Carbons,  53,  54,  57, 
61,  64, 71,  87,  207,  sqq. 
„  „     and  Carbons,  Apparatus 

for  Measuring,  208 
„  „    and  Carbons  with  Cored 

Carbons,    See    Cored 
Carbons 

„  „     and  Carbons  with  Hiss- 

ing, 61,  286 
„  „     and  Carbons,  Method  of 

Measuring,  209 

„  „     and  Carbons  with  Solid 

Carbons,     See     Solid 
Carbons 

„  „     and    Negative    Carbon, 

See  Neg.  Carbon  P.D. 

„  „    and  Positive  Carbon,  See 

Pos.  Carbon  P.D. 
„  „     and  Various  Electrodes, 

56 
P.D.  between  Carbons — 

„         with  Arc  under  Pressure,  67 
„         and   Changes   of   Current,   111, 

sqq.,  404,  435 

„        Const.,  Arc  with,  167, 171, 172,250 
„         Constant,  Cur.  and  I,  with,  167 
„        Constant,  Difficulty  of  Maintain- 
ing Arc  with,  171 
„         Constant,  Expts.  with,  170 
„         Constant,  for  given  I  with  Hiss- 
ing Arc,  279,  282,  288 
„        Constant,  Max.  I,  with,  167 
„        Constant,  Max.  Power  Efficiency 

with,  269,  273 
„        Constant,  Time  Variation  of  Cur. 

with,  172 

„    with  Cooled  Carbons,  47,  53,  86 
„    with  C.  Pos.  Carbons,  126,  sqq. , 

417,  422 

Cores  Affecting,  131,  139,  417 
„        and  Crater  Area,  153 
„        and  Crater  Depth,'  159 
„        and  Crater  Surface,  133,  422 

and  Cur.  47,  50,  100,  120  to  134, 

177,  sqq.,  242,  sqq.,  280,  422 
„        and  Cur.,  Curves  for,  101,  120, 
128,  129,  130,  132,  177,  187, 
242,  280,  423 


P.D.  between  Carbons— 

„  and  Cur.,  Curves  for,  with  C.  & 
S.  Carbons  compared,  132,  417 

„  and  Cur.,  Curves  for,  Discussion 
of,  123 

„  and  Cur.,  Curves  for,  with  En- 
closed Arcs,  304 

„  and  Cur.,  Curve  for,  a  Hyper- 
bola, 186 

„  and  Cur.,  Curves  for,  with  Res. 
Lines,  242,  sqq. 

„  and  Cur.,  Curves  for,  and  Res. 
of  Stability,  62,  242 

„  and  Cur.,  with  Hissing  Arcs, 
279,  sqq. 

„  and  Cur.  at  Hissing  Points,  282 
Cur.  and  I,  175,  192,  193,  198, 
204 

„  Cur,  and  Z,  Equations  for,  50, 
51,  64,  66,  67,  184,  186,  195, 
200,  202,  203 

„  Cur.  and  I,  Equations  for,  with 
Exploring  Carbon  in  Arc, 
230 

„  Cur.  and  I,  Equations  for,  Mean- 
ing of  Terms  in,  232 

„  Cur.,  and  Res.  of  Arc,  Simul- 
taneous Time  Change  of,  404, 
407 

„  Decreasing  with  Increasing  Cur., 
138 

„         and  Diameter  of  Carbons,  161 

„  Divided  by  Cur.,  and  Res.  of 
Arc,  402 

„        and  ~,  Curves  for,  80 

oA 
„        with  Exploring  Carbon  in  Arc, 

228,  235 
„        and  Hard  Crater  Ratio,  Curves 

for,  157 
,,         with  Hissing,  Cause  of  Fall  of, 

308 

„  „  C.  Pos.  Carbon,  291 

Fall  of,  39,  63,  278 
Fall  of,  and  I,  288 

„  „  S.  Pos.  Carbon,  285 

„        with  Hydrogen  Blown  at  Crater, 

306 
„        with  Oxygen   Blown  at  Crater, 

305 

„         Increasing  with  Increasing  Cur- 
rent, 141 
„        when  Independent  of  Cur.,  132, 

137,  141 

and  I.,  41,  48,  50, 55, 67, 136, 191 
„         and  l.t  Curves  for,  with  C.  Car- 
bons, 139,  140,  142,  144, 16? 


INDEX  TO  CONTENTS. 


475 


P.D.  between  Carbons — 

„         and  Z.,  Curves,  with   C.  and  S. 

Carbons  Compared,  142 
„         and  L,  Curves,  with  Crater  En- 
tirely in  Core,  147 
„         and  L,  Curves,  with  S.  Carbons, 

136,  144 
and  L,  Equation  for,  40  41,  49, 

50,  55,  67,  192 

„         and  L,  Equation  for,  with  Hiss- 
ing, 284 
„         and  L,  Equation  for,  at  Hissing 

Points,  282 

,,         Measurement  of,  99 
„         Minimum  with  given  I,  with  C. 

Carbons,  131,  135 
and  Negative  Carbon  P.D.,  225 
„         and  Particles  Shot  out  from  Car- 
bons, 84 
„         and  Positive  Carbon  P.D.,  215, 

222 

„         Steady,  Conditions  for,  102 
„         after  Striking  Arc,  102,  sqq. 
„         and  Surface  of  Crater,  133,  422 
„         with  Third  Carbon  in  Arc,  228, 

235 

„         Time  Change  of,  102,  sqq. 
„         Time    Change  of,    with    Const. 

Cur.  and  I,  97,  sqq.,  404 
„         Time  Change  of,  and  Cur.,  Ill 
„         Time  Change  of,  and  of  Cur.  and 

Res.,  404,  407 
„        Time  Change  of,  Curves  for,  103, 

105,  107,  109,  110,  113,  114 
„         Time   Change   of,   with  Hollow 

Pos.  Carbon,  108 
„        Time  Change  of,  Hump  on  Curve 

for,  107 
Time  Change  of,  and  I,  111,  114, 

434 
„        Time  Change  of,  and  Shapes  of 

Carbons,  108 

P.D.between  Hot  and  Cold  Carbon  Plates,57 
„         Negative  Carbon  and  Arc,   See 

Neg.  Carbon  P.D. 
,,         Positive    Carbon   and   Arc,   See 

Pos.  Carbon  P.D. 

P.Ds.,  Sum  of  Carbon,  and  Current,  226 
P.D.,  Kate  of  Fall  of,  Through  Arc,  59 

„      Vapour,  See  Vapour  P.D. 
Pepys,  23,  94 

Perry,  Ayrton  and,  40,  124 
Peukert,  42,  95,  193 
Pfaff,  22,  94 

Photographic  Power  of  Arc  Light,  31 
Photometer,  Universal,  330 
Photometry,  Assumptions  Made  in,  448 


Pitting  of  Crater  with  Hissing,  39,  292,  299 
Pointing  of  Exploring  Carbon  in  Arc,  57, 211 
Polar  Light  Curves,  320,  321,  344,  455 
„  „         and    Rousseau's    Fig- 

ures, 344,  452 
Poles,  Particles  Shot  out  from,  4,  28,  30, 

32,  84,  349 
Positive  Carbon  and  Arc,  P.D.  between, 

See  Pos.  Carbon  P.D. 
„  and  Arc,   Resistance  be- 

tween, 43,  50,  51,  88, 
392 

,,  Cored,  Appearance  of  Arc 

with,  6,  16,  60,  68,  419 

Cored,  and  ?Y,  78, 81, 418, 

424,  431 
„  Cored,  and  Hissing  Points 

133,  291,  417,  424 
„  Cored,  and  Largest  Silent 

Current,  133, 291,  417 
„  Cored.  P.D.  and  Cur.  with, 

126,  143,  417,  422 
„  Cored,   P.D.    of    Hissing 

Arc  with,  291 
„  Cored,  P.D.  and  I  with, 

130,  139 

„  Cored,  P.D.  Low  on  Strik- 

ing Arc  with,  103,  104, 

107 
„  Cored,    P.D.,     Minimum 

with,  131,  135 
„  Cored,  P.D.  Steady  with, 

102 
„  Cored,  P.D.  with  Sudden 

Change  of  Current,  115 
„  Cored,  Resistance  and  I, 

with,  164 
„  Crater  First  Observed  in, 

28 
„  Crater  Forming  in,  2,  28, 

393 
,,  and  Current  Density,  with 

Hissing  Arcs,  60 
„  Diameter  of,  and  Crater 

Ratios,  164 
„  Diameter  of,  and  Light 

374 
„  Flat,  Time  Variation  of 

P.D.  with,  106 
„  Heating      and      Cooling, 

Effect  of,  47,  53,  86 
„  P.D.  Compared  with  Total 

P.D.,  215,  222 
P.D.  not  a  Constant,  214 
P.D.  with  Cored  Carbons, 

235 


476 


INDEX  TO  CONTENTS. 


Positive  Carbon,  P.D.  and  Cur.,  214 

„  P.D.  and  Our.  and  I,  214, 

222,  400 
„  P.D.  and  Cur.  and  Power, 

220 
„  P.D.,  Definition  of,  212 

P.D.,  Fall  of,  at  Hissing, 

286 

P.D.  and  L,  216,  223,  236 
„  with  S.  Carbons,  214,  223, 

236 

Power,  220,  221 

„  „       Definition  of,  220 

Shape  of,  7,  13,  106,  294, 

298,  393 

„  Shape  of,  with  Hissing,  294 

„  Shape    of,    and    Hissing 

Laws,  298 

„  Shaping  of,  393 

„  Solid,  Appearance  of  Arc 

with,  6,  16,  25,  26,  27, 
31,   60,   68,  277,   292, 
300,  356,  358,  419 
„  Tip,  and  Crater  Area,  with 

Hissing,  61,  294 
„  Tubular,  Expts.  with,  108, 

305 

Potassium,  Carbons  steeped  in,  31 
Potential  Difference,  See  P.D. 
Potential  at  Different  Points  in  Arc,  57, 

64 

Rate  of  Fall  of  through  Arc,  59 
Power,  Candle,  See  Candle  Power 

„       and  Current,  Curves  for,  182,  196, 

200,  403 
„       and  Current,  Equation  for,  183, 191, 

195,  200,  204 
„       and  Current  and  I,  Equation  for, 

42,  183,  186,  188, 195,  200,  202 
,,       Distribution  of,  in  Arc,  370 
„       Efficiency  and  Cur.,  260 

and    E.M.F.,    261,    265, 

270 

>i  „         and  Hissing  Points,  261 

»  ,,          and  I,  260,  sqq. 

»  „          Maximum,  259,  sqq. 

»  „         Maximum,    with     given 

Cur.,  266,  270,  272 
»  ),         Maximum,    with     given 

E.M.F.,  265,  270 
»  jj         Maximum,  with  given  I, 

265 
»  »         Maximum,    with     given 

P.D.,269,273 

»>  )>          Maximum,    with     given 

Series  Resistance,  268, 
273 


Power  Expended  in  Arc,  259,  sqq. 
„  „  Carbon  Ends,  370 

„       Mist,  370,  403 
„      and  I,  178,  189,  195,  198 
„      and  I,  Curves  for,  180,  194,  199, 

373 
„       and  I,  Equation  for,  181,  193,  198, 

200 

„       and  Light  of  Arc,  30,  52,  370 
Pressure,  Arc  under,  67,  72,  83 

„        Internal,  of  Arc,  40 
Purple  Core  of  Arc,  2,  5,  6,  7,  57,  356,  392 

Quet,  33,  95 

Ray,  414 

Refraction  of  Light  by  Arc,  353 

„  ,,          „         Candle  Flame,  456 

Repulsion  of  Arc  bv  Exploring  Carbon,  58 

210 

Resistance  of  Arc,  Various  Experimenters, 

33,  37,  41,  43,  46,  49, 

50,  54,  71,  76,  124,  166, 

189,  193,  201,  398,  sqq. 

„          between  Arc  and  Carbons,  43, 

50,  51,  88,  392 
„         of  Arc  with  Cored  Carbons,  78, 

417,  421,  429 
„  „       and     Cross-section     of 

Mist,  398 

„  „       and  Cur.,  34,  37,  40 

„  „       Diminution  of  at  Hiss- 

ing, 288 

„  „  „  of     with 

Increase 
of  Cur., 
400 

„  „       and --,  when  equal,  406, 

410 

„  „       I,  See  Length  of  Arc 

,,  „       Measured   with    Added 

Alt.  Cur.,  49,  50,  54, 

71,  75,  406 
„       with  Metallic  Salts,  31 

46,  56,  78 
„  „       and  P.D.  divided  by  Cur., 

402 

„  „       and  Pressure  of  Atmo- 

sphere, 67 
„  „       Time   Change   of,  404, 

407 

„         Contact,  between  Arc  and  Car- 
bons, 43,  50,  51 

„         Lines,  Cutting   P.D.   and   Cur. 
Curves,  242,  sqq. 


Definition 


W6,  sq( 
of,  243 ' 


INDEX  TO  CONTENTS. 


477 


Resistance  Lines,   Tangent   to   P.D.-Cur. 

Curves,  245 
of  Mist,  418,  429 

,,          Negative,  See  Neg.  Resistance 
Resistance  in  Series  with  Arc — 

241,  246 
„        and  Cur.,  252 

Curi,  E.M.F.,  and  I,   245,  252, 

255 
„         and  E.M.F.  Fixed,  Max.  Power 

Efficiency  with,  268,  273 
„         Fixed,  Mio.  Cur.  and  Max.  I  with, 

253 
„         Functions  of,  250 

and  I,  252 

,,         and  I  Fixed,  Min  Cur.  with,  255 
„         Max.  with  given  /,  246 

Max.  with  given  I  andE.M.F.,  255 
Min.,  250,  251,  256,  274 
„         Necessity  for,  250 
Resistance  of    Stability,    P.D.   and    Cur., 

Curves  for,  62,  242 
„  of  Vapour  Film,  398 
„  „  „  Effect  of  Cores 

on,  421, 429 
Resistances,  Specific,  of  Different  Parts  of 

Arc,  392 
Ritter,  22,  94 
Rodgers,  Frith  and,  76,  96,  309,  406,  411, 

418 

Rossetti,  38,  95,  347 
Rotating  Disc  as  Electrode,  56 
Rotation  of  the  Arc,  69,  277,  292,  300,  322 

„     at  Magnet  Pole,  29 
Rousseau's  Figures,  335,  337,  344,  352 

„  „         and     Mean    Spherical 

Candle  Power,  344, 
452 
„  „        and  Polar  Light  Curves, 

344,  452 

Rowland,  Duncan  and  Todd,  66, 96, 188,  203 
Royal  Institution,  Battery  at,  26 
„  „  Davy's  Expts.  at,  21 

Salts,  Metallic,  Arcs  with,  31,  46.  56,  78 

Schreihage,  96,  374 

Scwendler,  37,  95,  141 

Seaton,  38,  302 

Series  Resistance,  See  Resistance  in  Series 

with  Arc 

„     Arc  Lamps  in,  387 
Shadow  of  the  Arc,  352 

„          Candle  and  Gas  Flames,  456 
Shape  of  Arc  with  C.  Pos.  Carbon,  6,  7,8,  81 
„          „    Horizontal,  26,  36 
„          „    with  S.  Pos.  Carbon,  6,  7,  8 
„    Vertical,  6,  7,  8,  31,  54,  60 


Shape  of  Arc  Vertical,  with  Hissing,  293 
„        Neg.  Carbon,  See  Neg.  Carbon 
„        Pos.  Carbon,  See  POP.  Carbon 
Shapes  of  Carbons,  8,  1C6,  293,  296    323 

393 

»  ,,         Change  of,  with  Sudden 

Change  of  Cur.,  14, 

106 

„  „         Explanation   of  Varia- 

tion in,  13, 14, 106, 393 
„  „         with  Hissing,  294 

Shepard,  Cross  and,  46,  95,  166,  198,  279 
Short  Arc,   Extra  Point  on  Neg.  Carbon 

with,  11 
„  Light    of,    Greater    than    of 

Longer  Arc,  325 
„  Mushroom  with  Hissing,   11, 

28,  86,  294,  300 

Silent  Arc  and  Hissing  Arcs,  Real  Differ- 
ence between,  297 

„  Largest  Cur.  for,  133,  278,  288 

Silliman,  28,  94,  349 
Sizes  of  Arcs,  Comparison  of,  with  S.  and  C. 

Carbons,  6,  15,  16,  419 
„      Carbons,  See  Diameters 
Small   Current,  Difficulty  of  Maintaining 

Arc  with,  176,  249 
„          Large  E.M.F.  needed  for,  249 
Smallest  Hissing  Current,  278,  288 
Smell  of  Arc,  28 
'  Soda,  Effect  of  on  P.D.  between  Carbons, 

56 
Sodium  Solutions,  Saturating  Carbons  with, 

31 

Soft  Carbon,  Proportion  of,  in  Crater,  144 
„     Crater  Ratio,  Calculation  of,  154 
„          „          „       Definition  of,  145 
„          „         „       and  Z,  146,  156 
Softening  of  Carbon,  28,  62,  347 
Solid  Carbon,  Light  from,  and  from  Core, 

377,  3b6 

„  Carbons  and  Cored,  Appearance  of 
Arc  with,  Compared,  6,  15, 
419 

,,  „        and  Cored,   P.D.  and  Cur. 

Curves    with,    Compared, 
132,  417 

„  „        and     Cored,    P.D.     and    I 

Curves    with,    Compared, 
142 

,,  „        and  Cored,  P.D.  for  Hissing 

Arcs  with,  Compared,  291 

,,  „        and   Cored,   Hissing  Points 

with,  Compared,  133,  291, 

417,  424 

„  „        and  Cross-section    of   Mist, 

16,  401,  419,  425 


478 


INDEX  TO  CONTENTS. 


Solid  Carbons  and  Cross-  section  of  Vapour 
Film,  404,  421 

Curves  for  .-r-and  Cur.  with 
79,434     5A 

Curves  for  ~  and  Frequency 
with,  437  5A 

Curves  for    —  -  and  I  with, 


434 


5A 


„  „        Curves  for  I  and  Kes.  with, 

166 
„          „       Curves   for   P.D.   and   Cur. 

with,  120,  175,  242,  280 
„       Curves  for  P.D.  and  I  with, 

138 
„  ,       Curves  for  Power  and  Cur. 

with,  181,   191,  196,  200, 

403 
„  „        Curves  for  Power  and  I  with, 

179,  193,  198,  373 
„  „       Light  Efficiency  and  I  with, 

380 
„          „       Light  Efficiency,  Maximum 

with,  380 

„          „       Negative  Value  of  —  -  with, 
oA 

54,  75,  81,  407,  sqq. 
„  „        Negative  Carbon  P.D.  with, 

217,  225 

„          „       P.D.,  Changes  with  Change 

of  Cur.  with,  112,  404,  434 

„          „       P.D.,  Never  Independent  of 

Cur.  with,  137 
„  „       P.D.  after  Striking  Arc  with, 

105,  107,  109,  110 
„  „       Positive   Carbon  P.D.  with, 

214,  223,  236 

„  „       Vapour  P.D,  with,  219,  229 

„     Particles  in  Arc,  84,  349 
Sound  of  Hissing,  Cause  of,  308 
Sounds  Emitted  by  the  Arc,  39,  46,  69, 

277,  279,  300 

Source  of  Heat  in  the  Arc,  393 
Sources  of  Light  in  the  Arc,  314 
Spark,  Electric,  and  Arc,  20 

„  „         Burning  Metals  with,  22 

„  „         with  Carbon  Terminals,  23 

„  „         with    Charcoal   Terminals 

20,24 

„  „         Continuous,  22 

„  „         Davy's  Experiments  with, 

20 

„  ,,         Striking  Arc  with,  30 

Sparks  Flying  out  from  Arc,  4 
Specific  Resistance  of  Arc,  Effect  of  Cores 
on,  422 


Specific  Resistance  of  Different  Parts  of 

Arc,  392 

Spots,  Bright,  on  Carbons,  4 
Stability  of  Arc,  Conditions  for,  62,  243, 

248 

Steady  ~,  Definition  of,  77 

Steadying  Resistance,  Functions  of,  250 
Steady  P.D.  with  given  Cur.  and  Z,  100, 

sqq. 

Stenger,  44,  64,  95,  96,  303 
Stokes,  351 

Striking  the  Arc  with  Cold  Carbons,  111 
„  „         with  Cored  Carbons,  Low 

P.D.,  103,  107 
„  „         Expansion  of  Gas  after, 

38,  45,  302 
Hissing  at,  301 
with  Hot  Carbons,  111 
with  Ley  den  Jar  Spark,  30 
P.D.  after,  102,  sqq. 
Time  Variation   of  P.D. 

after,  97,  sqq. 
„  „        Time  Variation  of   P.D. 

after,  Cause  of,  106 
Sturgeon,  29,  94 

Sublimation  of  Carbon  at  Crater,  346 
Sudden  Change  of  Cur.,  Effect  on  P.D.  of, 

112 
„  „         Effect  on  P.D.  of, 

Cause  of,  116 

„  „         Effect    oi,     on 

Shapes  of  Car- 
bons, 14,  106 

Sulphuric  Acid,  Arc  in,  31 
Surface  of  Volatilisation,  Area  of,  396 
Swinburne,  359 

Temperature  of  Arc,  38,  65,  68,  354 
„  Arc  Mist,  355 

Crater,  38,  61,  64,  65,  68, 
72,83,346,354,;359, 
393,  396,  sqq. 

„  „  in  Compressed  Gases,  83 

Temperatures  of  Electrodes,  29,  32,  38,  45, 

65,  392 

Thenard,  Fourcroy  and  Vauquelin,  22,  94 
Thermo-electric  E.M.F.  in  Arc,  39,  51,  66, 

90 

Thompson,  24,  64,  96,  202,  347,  458 
Thomson,  61,  96,  347 
Time  Variation  of  Cur.  with  Const.  P.D., 

171 

P.D.,  97,  sqq.,  404 
P.D.  and  Cur.,  Ill 

„  „  P.D.     and     Cur.     and 

Res.,  404,  407 


INDEX  TO  CONTENTS. 


479 


Time  Variation  of  P.D.,  Curves  for,  103, 
105,   107,   109,   110, 
113,  114 
„  „  with  Flat  Neg.  Carbon, 

108 
„  „  P.D.  with  Hollow  Pos. 

Carbon,  108 
„  „  P.D.,  Hump  on  Curve 

for,  107 

P.D.  and  I,  111,  114, 434 
„      „     P.D.  and  Shapes  of 

Carbons,  108 

„  „  P.D.      with      Sudden 

Change  of  Current, 
112,  404,  435 

„  „  Resistance,  404 

Tip  of  Negative  Carbon,  Shape  of,  2,  sqq., 

294,  323,  335,  393 
„      Positive  Carbon   and   Crater  Area, 

with  Hissing,  61,  294 
Tips  of  Carbons,  Lengths  of,  7 
Todd,  Duncan,  Rowland  and,  66, 96, 188,203 
Total   Light   and  Mean  Spherical  Candle 

Power,  See  Light 
Tromsdorff,  22,  23,  94 
Trotter,  69,  96,  277,  292,  300,  315,  338 
True  Resistance  of  Arc,  See  Resistance. 
Tubular  Pos.  Carbon,  Expts  with,  108,  305 

Upjjenborn,  50,  54,  96,  207,  211 

Uniform  Distribution  of  Crater  Light,  314, 

321,  347 
Unstable  Region  of  Hissing  Arcs,  133,  278, 

281 

„  „  „  Meaning 

of,  289 

Vacuum,  Arc  in,  25,  32,  47 

„         Discharge  and  Arc,  37,  44 

„  „          in  Various  Gases,  37 

Van  Breda,  32,  95 

Vapour,  Condensation  of,  in  Arc,  88,  355, 

391 
„      Conducting  Power  of,  392 


Vapour  from  Core,  421 
„       Film  in  Arc,  392 
„         „       and  Back  E.M.F.,  398 
„         „       Crater,  and  Volatilising  Sur- 
face, 396,  399 

„        „       Cross-section  of,  397,  421 
„         „  „  and  Cur., 421 

„         „  „  Effect         of 

Cores  00,421, 

425 

and  I.,  397 
„         „  „      Measurement  of, 

419 

„  „  Formation  of,  392 
„  „  Resistance  of,  398 
„  „  „  Cur.  and  I.,  400 

„         „  „  Effect  of  Cores 

on,  421,  429 

„         „       and  Mist  Compared,  355 
P.O.,  219,  229,  232,  236,  238 
„  „     Definition  of,  212 

„         Water,  round  Candle  Flame,  457 
Vauquelin,  Fourcroy  and  Thenard,  22,  94 
Violle,  65,  68,  96,  347,  354 
Volatilisation  of  Carbon  at  Crater,  28,  64, 

68,  84,  346,  347,  355,  392,  393 
Volatilising  Surface  of  Crater,  Area  of,  397 
„  „      Crater,     and    Vapour 

Film,  396,  399 

Voltaic  Pile,  Discovery  of,  19 
Voltmeter  used  in  Arc  Expts.,  209 
Volume  and  Cross-section  of  Arc,  395 
Von  Lang,  43,  50,  95,  406 

Walker,  29,  94 

Water  Electrode,  Arc  with,  33 

„     Vapour  round  Candle  Flame,  457 
Watlington,  414 
White  Spot,  Area  of,  345 

„         „      Definition  of,  210 

„        „      Light  of,  2,  4,  314,  345,  376 
Wilson,  72,  96 

„       and  Fitzgerald,  83,  96 

„       and  Gray,  459 


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